Editor Yilmaz SIMSEK Associate Editors Miloljub ALIJANIĆ,...

Editor Yilmaz SIMSEK

Associate Editors Miloljub ALBIJANIĆ, Mustafa ALKAN,

Irem KUCUKOGLU, Ortaç ÖNEŞ

Editor Yilmaz SIMSEK

Associate Editors Miloljub ALBIJANIĆ, Mustafa ALKAN,

Irem KUCUKOGLU, Ortaç ÖNEŞ

MICOPAM 2018 The Mediterranean International Conference

of Pure&Applied Mathematics and Related Areas

Dedicated to Professor Gradimir V. Milovanović on the Occasion of his 70th Anniversary

Antalya-Turkey, October 26–29, 2018 http://micopam2018.akdeniz.edu.tr/

Conference Venue: Sherwood Exclusive Kemer-ANTALYA

FOREWORD

Dear distinguished participants of the Mediterranean International Conference of

Pure&Applied Mathematics and Related Areas (MICOPAM 2018) held in Antalya, Turkey,

on October 26–29, 2018. On behalf of the Scientific and Organizing Committees, Welcome to

Turkey's pretty and historical Mediterranean resort town Antalya, which hosts our conference

MICOPAM2018 conference which dedicated to Professor Gradimir V. Milovanović on the

Occasion of his 70th Anniversary.

By the way Antalya, which is one of our historical cities, has been a source of inspiration for

many empires and civilizations. I hope you will visit some part of this pretty and historical city of

Turkey. In order to show some of the historical sites of this beautiful city, we have included an

excursion program to our conference.

This excursion includes a trip to Campus of Akdeniz University, Antalya Kaleici (Old Town),

Perge Ancient City (where the mathematician Apollonius lived), Aspendos Ancient Theatre, Side

Ancient City (where you see the splendid Agora, Theatre and Temples built in the 17th century

B.C.).

The idea of organizing this conference was appeared in 2017 at Belgrade, Serbia, while speaking

with Professor Gradimir V. Milovanović.

Brainstorming for conference name on napkin with Professor Gradimir V. Milovanović in 2017 at Belgrade, Serbia.

Our dreams are happening today because we are happy to have the opening of the conference

together. Thus, dear distinguished participants, you have given honor to us by attending our

conference: MICOPAM 2018.

From Left to Right: Professor Yilmaz Simsek, Professor Walter Gautschi, Professor Gradimir V. Milovanović

I would like to thank to the following my colleagues and students who helped me at every stage

of the Mediterranean International Conference of Pure & Applied Mathematics and Related

Areas:

Plenary Speakers

• Abdelmejid Bayad, (Université d’Evry Val d’Essonne, France)

• Walter Gautschi, (Purdue University, USA)

• Allal Guessab, (University of Pau, France)

• Satish Iyengar, (University of Pittsburgh, USA)

• Burcin Simsek, (Bristol-Myers Squibb Company, USA)

• Taekyun Kim, (Kwangwoon University, South Korea)

• Francisco Marcellán, (Universidad Carlos III de Madrid, Spain)

• Themistocles Rassias, (National Technical University of Athens, Greece)

• Lothar Reichel, (Kent State University, USA)

• Ekrem Savas, (Rector of Uşak University, Turkey)

• Hari M. Srivastava, (University of Victoria, Canada)

Local Organizing Committee: (including especially Co-Chairman Prof. Dr. Mustafa Alkan, Prof.

Dr. Veli Kurt, Conference Secretary Asst. Prof. Dr. Irem Kucukoglu, Dr. Ortaç Öneş, Dr.

Neslihan Kilar, Dr. Busra Al, Asst. Prof. Dr. Fusun Yalcin, Asst. Prof. Dr. Ayse Yilmaz Ceylan,

Assoc. Prof. Dr. Ahmet Aykut Aygunes, Dr. Burak Kurt); my precious family: (my wife Saniye,

my daughters Burcin and Buket), Professor Gradimir V. Milovanović; besides academic staff of

Akdeniz University: Rector Prof. Dr. Mustafa Ünal and Vice Rector Prof. Dr. Erol Gürpınar,

Dean of Faculty of Science Prof. Dr. Ahmet Aksoy, some staff of Department of Mathematics;

Prof. Dr. Ömer Colak, Prof. Dr. Gurhan Yalcin, Prof. Dr. Niyazi Ugur Kockal, and also other

friends whose names that I did not mention here.

As for mathematics; Mathematics is the common heritage of everyone; Mathematics is the

common language of the world that is always passed from generation to generation by refreshing.

It would be appropriate to say the following:

https://www.maths.univ-evry.fr/pages_perso/bayad/

http://www.cs.purdue.edu/people/wxg

https://www.researchgate.net/profile/Guessab_Allal/contributions

http://www.stat.pitt.edu/people/satish-iyengar

https://www.linkedin.com/in/burcin-simsek-00174679

https://zbmath.org/authors/?q=ai:kim.taekyun

http://gama.uc3m.es/index.php/fmarcellan.html

http://math.ntua.gr/~trassias/

http://www.math.kent.edu/~reichel/

http://ekremsavas.com/

http://www.math.uvic.ca/~harimsri/

In addition to the poetic and artistic aspect of mathematics, mathematics has such a spiritual,

magical and logical power, all-natural science and social science cannot breathe and survive

without mathematics.

Mathematics is such a branch of science that other sciences cannot develop without it. Therefore,

Mathematics, which is the oldest of Science, has contributed fundamentally to the development of

our world civilizations. So, we can enter into the science and technology centers using the power

of mathematics and its branches. So, mathematics and its branches create the possibility of

bridgework and communication between the Natural Sciences and the Engineering Sciences as

well as the Economic and also Social Science.

The aim of the conference is to bring together leading scientists of the pure and applied

mathematics and related areas to present their researches, to exchange new ideas, to discuss

challenging issues, to foster future collaborations and to interact with each other. In fact, the main

purpose of this conference is to bring to the fore the best of research and applications that will

help our world humanity and society. Due to the valuable idea of the MICOPAM2018, this

conference welcomes speakers having talks whose contents mainly related to the following two

subjects: Pure and Computational and Applied Mathematics, Statistics, Mathematical Physics

(related to p-adic Analysis, Umbral Algebra and Their Applications), Analysis Algebra Linear

and Multi-linear Algebra, Clifford Algebras and Applications, Real and Complex Functions,

Orthogonal Polynomials, Special numbers and Functions, Fractional Calculus, q-calculus,

Number theory, Combinatorics, Approximation theory, Optimization Integral Transformations,

Equations and Operational Calculus, Partial Differential Equations, Geometry and Its

Applications, Numerical Methods and Algorithms, Probability and Statistics and their

Applications, Scientific Computation Mathematical Methods in Physics and in Engineering

Mathematical Geosciences.

To summarize my speech, this conference has provided a novel opportunity to our distinguished

participants to meet each other and share their scientific works and friendships in the above areas.

I am delighted to note that all participants have free and active involvement and meaningful

discussion with other participants during the conference at the hotel Sherwood Exclusive Kemer,

which contains all shades of green and yellow, around the Taurus Mountains and decorated with

turquoise color of the Mediterranean Sea.

It is my great pleasure to thank Professor Gradimir V. Milovanović, because this conference is

dedicated to his 70th birthday at Antalya. Happy Birth Day Professor Gradimir V. Milovanović. I

hope that his life will be with health and happiness. It is my great pleasure to thank again local

organizing committee Consequently, I send my thanks to all distinguished invited speakers, and

all participants.

PROF. DR. YILMAZ SIMSEK

Head of the Organizing Committee of MICOPAM 2018

Department of Mathematics, Faculty of Science,

Akdeniz University, TR-07058 ANTALYA-TURKEY, Tel: +90 242 310 23 43,

Email : [email protected], [email protected]

mailto:[email protected]

mailto:[email protected]

PREFACE

In the “Abstract Booklet of MICOPAM 2018”, we published only abstract of the presented

papers. On the other hand, in the Proceedings Book of MICOPAM 2018 with ISBN 978-86-

6016-036-4, we published all invited speaker’s papers or abstracts and also full-text of

Proceedings with at least 3 pages and at most 5 pages long, of participants who signed

“COPYRIGHT RELEASE FORM FOR MICOPAM 2018 of CONFERENCE

PROCEEDINGS”. In the Proceedings Book of MICOPAM 2018, we gave some information

about the name of "The Mediterranean International Conference of Pure & Applied

Mathematics and Related Areas (MICOPAM 2018)". That is, in this book, we mentioned that

the Mediterranean Sea related to almost all the countries, because all seas and the oceans are

connected. This conference was dedicated to the 70th birthday of the respected and

distinguished Professor Gradimir V. Milovanović. The main aim of this conference is to give

connection between many areas of sciences including physical mathematics and engineering,

especially all branches of mathematics. A few of these areas can be given as follows: Pure and

Computational and Applied Mathematics, Statistics, Mathematical Physics (related to p-adic

Analysis, Umbral Algebra and Their Applications).

Another important purpose of the Mediterranean International Conference of Pure & Applied

Mathematics and Related Areas (MICOPAM 2018) is to bring together scientists who are

experts in the following areas and also to provide joint projects and cooperation: Various

fields of Mathematics, (Mathematical) Physics, Engineering and related areas such as

Analysis, Non-linear Analysis, Integral transforms, Number Theory, p-adic Analysis and

Applied Algebra, Special Functions, q-analysis and Discrete Mathematics, Probability and

Statistics, Mathematical Physics and their applications. As for our purpose is also to bring

together theoretical, numerical and apply analyst, number theorists, (quantum) physicist

working in above mentioned branches of science (Mathematics, Physics, Engineering).

As for the scope of the Abstract Booklet of MICOPAM 2018, it consists of foreword, about

the MICOPAM 2018, conference committees, short biography of Professor Gradimir V.

Milovanović and short abstracts of presented papers of some participants. The Abstract

Booklet of MICOPAM 2018 may be used for above mentioned branches of science

(Mathematics, Physics, Engineering). Consequently, this book is suitable for researchers.

Editor

Yilmaz SIMSEK

Associate Editors

Miloljub ALBIJANIĆ, Mustafa ALKAN, Irem KUCUKOGLU and Ortaç ÖNEŞ

Acknowledgments: Thank to Prof. Dr. Gradimir V. Milovanović, Prof. Dr. Miloljub

Albijanić, Prof. Dr. Mustafa Alkan, Asst. Prof. Dr. Irem Kucukoglu, and Dr. Ortaç Öneş who

provided most valuable contribution on preparing this book with their LaTeX&PDF processes

and Cover Page of the Abstract Booklet of MICOPAM 2018.

Editor

Yilmaz SIMSEK

ABOUT CONFERENCE

The Mediterranean International Conference of Pure&Applied Mathematics and Related

Areas Dedicated to Professor Gradimir V. Milovanović on the Occasion of his 70th

Anniversary Antalya-Turkey, October 26–29, 2018.

The Mediterranean International Conference of Pure&Applied Mathematics and Related

Areas (MICOPAM 2018) will be held in Antalya, Turkey, on October 26–29, 2018. The event

will be held over four days, with presentations delivered by researchers from the international

community, including presentations from keynote speakers and state-of-the-art lectures. The

aim of the conference is to bring together leading scientists of the pure and applied

mathematics and related areas to present their researches, to exchange new ideas, to discuss

challenging issues, to foster future collaborations and to interact with each other.

The conference is dedicated to the renowned mathematician Prof. Dr. Gradimir V.

Milovanović on the occasion of his 70th anniversary.

Prof. Dr. Gradimir V. Milovanović

Prof. Dr. Gradimir V. Milovanović, born in Zorunovac, Serbia, 2 January 1948, is one of

the the world leading scientists in the field of numerical analysis, approximation theory and

special functions, a longtime professor at the University of Niš, Serbia, and a member of the

Serbian Academy of Sciences and Arts.

This conference welcomes speakers whose talk or poster contents are mainly related to the

following two subjects:

• Pure and Computational and Applied Mathematics & Statistics

• Mathematical Physics (related to p-adic Analysis, Umbral Algebra and Their Applications)

http://www.mi.sanu.ac.rs/~gvm/

PLENARY SPEAKERS

• Abdelmejid Bayad, (Université d’Evry Val d’Essonne, France)

• Walter Gautschi, (Purdue University, USA)

• Allal Guessab, (University of Pau, France)

• Satish Iyengar, (University of Pittsburgh, USA)

• Burcin Simsek, (Bristol-Myers Squibb Company, USA)

• Taekyun Kim, (Kwangwoon University, South Korea)

• Francisco Marcellán, (Universidad Carlos III de Madrid, Spain)

• Themistocles Rassias, (National Technical University of Athens, Greece)

• Lothar Reichel, (Kent State University, USA)

• Ekrem Savas, (Rector of Uşak University, Turkey)

• Hari M. Srivastava, (University of Victoria, Canada)

COMMITTEES

Honorary Presidents

• Prof. Dr. Mustafa UNAL, (Rector of Akdeniz University, Turkey),

• Prof. Dr. Ahmet AKSOY, (Dean of Faculty of Science Akdeniz University, Turkey)

Head of The Organizing Committee

• Prof. Dr. Yilmaz Simsek, (Akdeniz University, Turkey)

Chairman of The Organizing Committee

• Prof. Dr. Mustafa Alkan, (Akdeniz University, Turkey)

MICOPAM 2018 Conference Secretary

• Asst. Prof. Dr. Irem Kucukoglu, (Alanya Alaaddin Keykubat University, Turkey)

Scientific Committee

• Mustafa Alkan, Turkey,

• Ravi Agarwal, USA,

• Abdelmejid Bayad, France,

• Nenad Cakić, Serbia,

• Ismail Naci Cangul, Turkey,

• Abdullah Cavus, Turkey,

• Ahmet Sinan Cevik, Turkey,

• Junesang Choi, South Korea,

• Dragan Djordjević, Serbia,

• Allal Guessab, France,

• Mohand Ouamar Hernane, Algeria,

• Satish Iyengar, USA,

• Taekyun Kim, South Korea,

• Miljan Knežević, Serbia,

• Veli Kurt, Turkey,

• Branko Malešević, Serbia,

• Francisco Marcellán, Spain,

• Giuseppe Mastroianni, Italy,

• Gradimir V. Milovanović, Serbia,

• Tibor Poganj, Croatia,

• Abdalah Rababah, Jordan,

• Themistocles Rassias, Greece,

• Lothar Reichel, USA,

• Ekrem Savas, Turkey,

• Yilmaz Simsek, Turkey,

• Miodrag Spalević, Serbia,

• Hari M. Srivastava, Canada,

• Marija Stanić, Serbia

Local Organizing Committee

• Busra Al,

• Mustafa Alkan,

• Ahmet Aykut Aygunes,

• Secil Bilgic,

• Secil Ceken,

• Ayse Yilmaz Ceylan,

• Neslihan Kilar,

• Irem Kucukoglu,

• Burak Kurt,

• Ortaç Öneş,

• Rahime Dere Pacin,

• Mustafa Ozdemir,

• Mehmet Uc,

• Yilmaz Simsek,

• Buket Simsek,

• Fusun Yalcin.


http://www.cs.purdue.edu/people/wxg



https://www.linkedin.com/in/burcin-simsek-00174679







http://www.drmustafaunal.com/

http://biyo.fen.akdeniz.edu.tr/tr.i108.prof-dr-ahmet-aksoy

http://aves.akdeniz.edu.tr/ysimsek/yayinlar

http://aves.akdeniz.edu.tr/alkan/yayinlar

https://scholar.google.com.tr/citations?user=oyIqmp8AAAAJ&hl=tr

http://aves.akdeniz.edu.tr/alkan/yayinlar

http://www.tamuk.edu/artsci/math/faculty/agarwal.html


http://matematika.etf.bg.ac.rs/ljudi/n_cakic.htm

http://www.ismailnacicangul.com/index.php/contact

https://www.researchgate.net/profile/Abdullah_Cavus

http://www.ahmetsinancevik.com/

http://junesangchoi.com/

http://operator.pmf.ni.ac.rs/licne_prezentacije/DDjordjevic/Dragan_Djordjevic_english.htm


https://www.researchgate.net/profile/M_Hernane



https://www.researchgate.net/profile/Miljan_Knezevic

https://scholar.google.com.tr/citations?user=pp7Oc7kAAAAJ&hl=tr&oi=ao

http://home.etf.rs/~malesevic/


http://oldwww.unibas.it/utenti/mastroianni/curriculumVitae.html

http://www.mi.sanu.ac.rs/~gvm/

http://www.pfri.uniri.hr/~poganj

http://www.just.edu.jo/eportfolio/Pages/Default.aspx?email=rababah




http://aves.akdeniz.edu.tr/ysimsek/yayinlar

http://www.mas.bg.ac.rs/fakultet/nastavnici/189


https://imi.pmf.kg.ac.rs/index.php?id=67

SHORT BIOGRAPHY OF PROF. GRADIMIR V. MILOVANOVIĆ

Prof. Gradimir V. Milovanović, full member of the Serbian Academy of Sciences and Arts

(SASA), was born on 2nd January, 1948, in Zorunovac, municipality of Knjaževac, to father

Vukašin and mother Vukadinka, b. Savić. He finished primary school in his birth place, and

high school of Natural-mathematical specialization in Knjaževac. He graduated from the

Faculty of Electronics in Niš, in 1971, at the department of Computer Sciences. Postgraduate

studies in the area of Applied Mathematics he completed in 1974, and in 1976, defended the

PhD thesis and thus acquired the scientific degree of Doctor of Mathematical Sciences.

At the Faculty of Electronics in Niš, he passed all degrees, from an assistant (1971), assistant

professor (1976), associate professor (1982), to professor (1986). In 2006 he was elected a

Corresponding Member of SASA and a full member in 2012. Since 2014 Prof. Gradimir V.

Milovanović is retired (for detailed biographical and bibliographical data see:

http://www.mi.sanu.ac.rs/~gvm/).

In his teaching career of several decades, he taught at the Electronic Faculty in Niš, and other

faculties in Serbia (Faculty of Electrical Engineering and Faculty of Mathematics in Belgrade,

Faculty of Mechanical Engineering and Faculty of Civil Engineering in Niš, Faculty of

Sciences and Mathematics in Niš, Kragujevac, etc.). He held courses at graduate, master, and

doctorate studies, including Numerical Analysis, Approximation Theory, Special Functions,

Operational Research, as well as numerous subjects in the area of Computer Science and

Information Technology. He was a visiting professor at Purdue University (USA), Universite

de Pau (France), and Universita di Basilicata, Potenza (Italy). He published 23 text-books,

among them his Numericka analiza (Numerical Analysis) in three volumes (Научна књига,

Belgrade; first edition 1985 was the first complete text book on this subject in ex Yugoslavia,

which has been widely used by numerous generations of students.

In the scientific research he published 7 monographs and about 350 scientific papers (over

150 in journals from the SCI list), with several thousand citations. Most significant

monograph works of Milovanović are Topics in Polynomials: Extremal Problems,

Inequalities, Zeros (coauthors: D. S. Mitrinović and Th. M. Rassias), published at over 800

pages by World Scientific (Singapore, 1994) and known in the world as „Bible of

Polynomials“ and the monograph Interpolation Processes – Basic Theory and Applications

(cоаuthor: G. Mastroianni) by Springer Verlag, 2008. He supervised 13 Ph.D. Theses and 16

Master Theses, as well as many scientific research projects, including the international

projects SCOPES and TEMPUS. As a reviewer of scientific projects, he worked for the

Ministry of Science of Serbia, Italy and Montenegro. He participated in the work of

commissions for doctorate theses and promotion of professors in many countries (France,

Italy, Morocco, Cyprus, Australia, India). He is the founder of the scientific journal Facta

Universitatis: Series Mathematics and Informatics at the University of Niš and its first Editor-

in-Chief. He is Editor-in-Chief of the journals: Journal of Inequalities and Applications

(Springer), Publication Mathematique Belgrade, Bulletin (SANU); Associate Editor of the

journals: Optimization Letters (Springer), Applied Mathematics and Computation (Elsevier),

as well as a member of the editorial board of a number of journals in Serbia (AADM,

FILOMAT, ... ), Romania, Bulgaria, Armenia and India. As an invited lecturer he took part in

numerous international conferences worldwide, eg. Bulgaria (Sofia, Borovec), Poland

(Warsaw), Hungary (Miskolc, Budapest), USA (Purdue University), Germany (Oberwolfach),

Romania (Cluj-Napoca, Timisoara), Italy (Vico Equense, Acquafredda di Maratea, Falerna,

Erice, Alba di Canazei), Singapore, Norway (Røros), Denmark (Copenhagen), France

(Marseille), Spain (Granada, Seville, Ubeda), South Africa (Stellenbosch, Port Elizabeth),

Morocco (Marrakech, Casablanca), Brazil (Campos do Jordao), South Korea (Gyeongju,

Seoul), Turkey (Antalya, Kirsehir, Kusadasi-Aydin), etc.

Milovanović performed various relevant functions: the Head of the Department of

Mathematics at the Faculty of Electronics in Niš (1983–2002), Vice Rector of the University

of Niš (1989–1991), the Dean of the Faculty of Electronics in Niš (2002–2004), the Rector of

the University of Niš (2004–2006), member of the Executive Board of Electric Power

Industry of Serbia (2004–2006), the President of the National Council of Serbia for Science

and Technology Development (2006–2010), the President of the Scientific Committee for

Msathematics, Computer Sciences and Mechanics (2010–2015), etc. He is also a member of

several important international organisations, among which are AMS (American

Mathematical Society), SIAM (Society for Industrial and Applied Mathematics) and GAMM

(Gesellschaft für Angewandte Mathematik und Mechanik). Since 2016 he is the Secretary of

the Department of Mathematics, Physics and Geo Sciences in SASA.

➢Abdelmejid Bayad, France➢Walter Gautschi, USA➢Allal Guessab, France➢Satish Iyengar, USA➢Burcin Simsek, USA➢Taekyun Kim, South Korea

➢Mustafa Alkan, Turkey (Co-Chairman)➢Ravi Agarwal, USA➢Abdelmejid Bayad, France➢Nenad Cakić, Serbia➢Ismail Naci Cangul, Turkey➢Abdullah Cavus, Turkey➢Ahmet Sinan Cevik, Turkey➢Junesang Choi, South Korea➢Dragan Djordjević, Serbia➢Allal Guessab, France➢Mohand Ouamar Hernane, Algeria➢Satish Iyengar, USA➢Taekyun Kim, South Korea➢Miljan Knežević, Serbia➢Veli Kurt, Turkey➢Branko Malešević, Serbia➢Francisco Marcellán, Spain➢Giuseppe Mastroianni, Italy➢Gradimir V. Milovanović, Serbia➢Tibor Poganj, Croatia➢Abdalah Rababah, Jordan➢Themistocles Rassias, Greece➢Lothar Reichel, USA➢Ekrem Savas, Turkey➢Yilmaz Simsek, Turkey (Chairman)➢Miodrag Spalević, Serbia➢Hari M. Srivastava, Canada➢Marija Stanić, Serbia

Honorary Presidents➢Prof.Dr. Mustafa UNAL, (Rector of Akdeniz University, Turkey)➢Prof.Dr. Ahmet AKSOY, (Dean of Faculty of Science Akdeniz University, Turkey)Head of The Organizing Committee➢Prof.Dr. Yilmaz Simsek, (Akdeniz University, Turkey)Chairman of The Organizing Committee➢Prof.Dr. Mustafa Alkan, (Akdeniz University, Turkey)Conference Secretary➢Asst. Prof. Dr. Irem Kucukoglu,(Alanya Alaaddin Keykubat University, Turkey)Local Organizing Committee➢Busra Al➢Ahmet Aykut Aygunes➢Secil Bilgic➢Secil Ceken➢Ayse Yilmaz Ceylan➢Neslihan Kilar➢Irem Kucukoglu➢Burak Kurt➢Mustafa Ozdemir➢Ortaç Öneş➢Rahime Dere Pacin➢Mehmet Uc➢Buket Simsek➢Fusun Yalcin

➢Francisco Marcellán, Spain➢Themistocles Rassias, Greece➢Lothar Reichel, USA➢Ekrem Savas, Turkey➢Hari M. Srivastava, Canada

Dedicated to Professor Gradimir V. Milovanović on the Occasion of his 70th Anniversary

Antalya-Turkey, October 26–29, 2018http://micopam2018.akdeniz.edu.tr/

Conference Venue: Sherwood Exclusive Kemer-ANTALYA

MICOPAM 2018The Mediterranean International Conference

of Pure&Applied Mathematicsand Related Areas

Scientific Committee Plenary SpeakersOrganizing Committee

ABSTRACT BOOKLET OF MICOPAM 2018

Abstract Booklet of The Mediterranean International

Conference of Pure&Applied Mathematics and

Related Areas 2018

(MICOPAM 2018)

Contents

1 CONTRIBUTED SPEAKERS 1

Jain-Appell Operators and Their Approximation Properties 2Mehmet Ali Ozarslana

Grobner-Shirshov bases for some structures 3Firat Atesa, Ahmet Sinan Cevikb, Eylem Guzel Karpuzc

Multiple zeta values at the non-positive integers 5Boualem Sadaouia

Classical character of 2-OPS 6Ali Krelifa1

On the Truncation Error in the Solution of Dirichlet Problem for Laplace’sEquation in Plane by Finite Differences Using Hexagonal Grid 8

Suzan C. Buranaya

One D(4)-Diophantine triples of Fibonacci numbers. 9Salah Eddine Rihane a, Mohand Ouamar Hernaneb, Alain Togbe c

Numerical solution of a free surface flow problem over an obstacle 10Dahbia Hernane a, Samira Beyoud b

Multiple orthogonal polynomials on the semicircle 11Marija P. Stanica

On The Partially q-Poly-Euler Polynomial of The Second Kind 12Veli Kurta

Notes On The Poly-Korobov Type Polynomials and Related Polynomi-als 13

Burak Kurta

Dedicated to Professor G. Milovanovic i Antalya-TURKEY


Multiple orthogonal trigonometric polynomials of semi-integer degreeand the corresponding quadrature rules 14

Gradimir V. Milovanovica, Marija P. Stanicb, Tatjana V. Tomovicb

Tensors and the Clifford Algebra: Special case Pinched Tensor Product 15Yousuf Alkhezi

Efficient optimal families of higher-order iterative methods with localconvergence 17

Ramandeep Behla , Jose Manuel Gutierrezb , I. K. Argyrosc , Ali Saleh Alshomrania

Numerical Solution of Ordinary Differential Equations and Burger-Huxley Second Order Partial Differential Equations using Splines 18

Abdallah Rababah1

A family of higher-order iteration functions for the solutions of nonlin-ear models 19

Ramandeep Behla, I.K. Argyrosb, Ali Saleh Alshormania, Samaher KhalafAlharbia

On the ω−Multiple Meixner Polynomials of First Kind 20Sonuc Zorlu Ogurlua , Ilkay Elidemirb

On the ω−Multiple Charlier Polynomials 21Mehmet Ali Ozarslana , Gizem Baranb

Domination on hyperbolic graphs 22Rosalıo Reyesa , Jose M. Rodrıgueza , Jose M. Sigarretab,c , Marıa Villetad

Structure theorem for quasihyperbolic metric 24Jesus Gonzaloa, Ana Portillab, Jose M. Rodrıguezc, Eva Tourısa

On the factorisation of p-adic meromorphic functions; primality andpseudo-primality 26

Zerzaihi Tahara, Boutabaa Abdelbakib, Saoudi Bilalc

Relations of the geometric-arithmetic index with some topological in-dices 27

Ana Granadosa, Ana Portillaa, Jose M. Rodriguezb, Jose M. Sigarretac

On Double Rotations in Minkowski Space-time 29Melek Erdogdua, Mustafa Ozdemirb

Generalized Darboux Frame of Curves on Hypersurfaces in EuclideanFour Space 31

Melek Erdogdua

Weak Solutions for Nonlinear Fractional Differential Equations in Ba-nach Spaces 33

Fatima Zohra Mostefaia , Mouffak Benchohrab

On the Taketa inequality 34Burcu Cınarcıa, Temha Erkocb

Dedicated to Professor G. Milovanovic ii Antalya-TURKEY


Anti–synchronization of nonidentical fractional order hyperchaotic sys-tems 35

Abedel-Karrem Alomaria

Slightly ω − (μ, σ)-irresolute functions between generalized topologicalspaces 36

Samer Al Ghour1 , Abeer Al-Nimer2

Approximation of fixed points of nonlinear contractions in metric space 37Petko D. Proinova

On the Partially q-Poly-Bernoulli Numbers and Polynomials 38Secil Bilgic1, Veli Kurt2

Some operator inequalities and their applications 39Hamdullah Basaran1 , Mehmet Gurdal2 , Aysenur Guncan3

Advanced refinements of Hilbert-type inequalities in a difference form 41Mario Krnic1 , Tserendorj Batbold2 , Josip Pecaric3

Orthogonal polynomials and the mismatch theorem 42Stefano Pozza1 , Miroslav Pranic2 , Zdenek Strakos3

A Generalization of the Suborbital Graphs Generating Fibonacci Num-bers for the Subgroup Γ3 43

Seda Ozturk

New asymptotic expansions and approximation formulas for the facto-rial function 44

Tomislav Buric1

Addition Behavior of an Arf Numerical Semigroup 45Nesrin Tutas1 , Nihal Gumusbas2

Maximal commutative subalgebras of a Grassmann algebra 46Ho-Hon Leung1 , Victor Bovdi2

Extended incomplete version of hypergeometric functions 47Mehmet Ali Ozarslana , Ceren Ustaoglub

A note on Pointwise Convergence by Nonlinear Singular Integral Op-erators in Mobile Interval 48

Mine Menekse Yılmaz1

Some basic properties of the generalized bi-periodic Fibonacci and Lu-cas sequences 50

Elif Tan1

Jungck Type Fixed Point Results in Rectangular Soft Metric Space 51Simge Oztunc1 , Ali Mutlu2 , Sedat Aslan3

Relatively-normal Slant Helices and Their Characterizations 53Nesibe Macit1, Mustafa Duldul1

Dedicated to Professor G. Milovanovic iii Antalya-TURKEY


On entropies and some special functions 54Julije Jaksetic

On generalized f-divergences through matrix inequality approach 55Dora Pokaz1

Some local forms of new convergences and one type of Arzela Theorem 56Doris Doda1 , Agron Tato2

Fuzzy Soft Multi LA-Γ-Semigroups 58Canan Akın1

On the comparison of two different one-parametric generalizations ofthe logarithmic mean 60

Mirna Rodic1

Lidstone interpolation of composition function and Steffensen-type in-equalities 61

Asfand Fahad1 , Josip Pecaric2 , Marjan Praljak3

On Levinson’s inequality involving averages of 3-convex functions 62Ana Vukelic

Generalized Block Anti-Gauss Quadrature Rules 63Hessah Alqahtani1 , Lothar Reichel2

On Suborbital Graphs and Matrices with Even Fibonacci and LucasNumbers 64

Ummugulsun Akbaba1 , Ali Hikmet Deger2

Lorentz-Marcinkiewicz Property of Direct Sum of Operators 66Pembe Ipek Al

Star Saturation Number of Random Graphs 67B. Tayfeh-Rezaie

On Generalization of Group Rings and Group Modules over G-sets 68Mehmet Uc1

Some Results On Prime And 2-Absorbing Primary C-Ideals Of Multi-plicative Hyperrings 69

Neslihan Aytac1 , Gursel Yesilot2

On the stabilizer of two dimensional vector space of 27-dimensionalmodule of type E6 over a field of characteristic two 70

Yousuf Alkhezi1 , Mashhour Bani Ata2

Coefficient estimates for a class containing quasi-convex functions ofcomplex order 72

Oznur Ozkan Kılıc

A note on a subclass of analytic functions 73Oznur Ozkan Kılıc

Dedicated to Professor G. Milovanovic iv Antalya-TURKEY


Minimax approximations and some analytic inequalities with a param-eter 74

Branko Malesevic1, Tatjana Lutovac1, Marija Rasajski1, Bojan Banjac2

2 POSTER PRESENTATIONS 75

Optical properties of Er3+ doped fluoride single crystal 76S. Khiari1,2 , M. Diaf2 , E. Boulma2 , C. Bensalem2

Spectroscopic Study of Er3+ Doped CdF2 Single Crystal 77F. Bendjedaa1 , M. Diaf2

On the coefficient bounds for general subclasses of close-to-convex func-tions of complex order 78

Serap Buluta

Existence of Positive Solutions for a Class of Second Order ImpulsiveBoundary Value Problems on an infinite interval in Banach Spaces 80

Ilkay Yaslan Karaca1 , Aycan Sinanoglu Arısoy2

Dedicated to Professor G. Milovanovic v Antalya-TURKEY


1 CONTRIBUTED SPEAKERS

Dedicated to Professor G. Milovanovic 1 Antalya-TURKEY


Jain-Appell Operators and Their

Approximation Properties

Mehmet Ali Ozarslana

Abstract

In this paper, we introduce Jain-Appell operators, which includes Jain Petheoperators and presumably new families of approximation operators of Appelltype. We investigate their weighted approximation properties and compute theerror of approximation by using certain Lipschitz class functions. Finally, anasymptotic expansion of Voronovskaya type is obtained.

2010 Mathematics Subject Classifications : 41A17, 41A35, 41A36Keywords: Jain-Appell operators, Szasz-Mirakjan operators , modified Lipschitz

type functions, Voronoskaja type asymptotic formula.

References

[1] C. Atakut and I Buyukyazıcı, Approximation by Modified Integral TypeJakimovski-Leviatan Operators, Filomat 30:1 (2016), 29–39.

[2] G.C. Jain and S.Pethe, On the generalizations of Bernstein and Szasz Operators,Nanta Math. 10. (1977), 185-193.

[3] A. Jakimovski, D. Leviatan, Generalized Sz´asz operators for the approximationin the infinite interval. Mathematica (Cluj) 11 (34) (1969) 97–103.

[4] O. Szasz, Generalization of S. Bernstein’s polynomials to the infinite interval, J.Res. Nat. Bur. Standards 45 (1950) 239–245.

aDepartment of Mathematics, Faculty of Arts and Science East-

ern Mediterranean University, Famagusta, North Cyprus via Mersin 10,

Turkey.

E-mail : [email protected]



Grobner-Shirshov bases for some structures

Firat Atesa, Ahmet Sinan Cevikb, Eylem Guzel Karpuzc

Abstract

The theories of Grobner and Grobner-Shirshov bases were invented indepen-dently by A. I. Shirshov [9] for non-commutative and non-associative algebras,and by H. Hironaka [8] and B. Buchberger [6] for commutative algebras. Inthe paper [9], there were proved the algorithmic decidability of word problemand the Freiheitsatz theorem for any one-relator Lie algebra. The technique ofGrobner-Shirshov bases is proved to be very useful in the study of presentationsof associative algebras, Lie algebras, semigroups, groups and Ω-algebras by con-sidering generators and relations (see, for example, the book [2] written by L.A. Bokut and G. Kukin, survey papers [3, 4, 5]). Furthermore, [7], Grobner-Shirshov bases for the Chinese monoid were defined. The reader is referred to[1] for a list of some other recent papers about Grobner-Shirshov bases.

In this talk, we present Grobner-Shirshov bases for some monoid and semi-group structures. It is well known that this basis gives an algorithm for gettingnormal forms, and hence an algorithm for solving the word problem in thosestructures.

2010 Mathematics Subject Classifications:13P10, 16S15, 20M05.Keywords: Grobner-Shirshov bases, normal form, word problem.

References

[1] F. Ates, A. S. Cevik, E. G. Karpuz, Grobner-Shirshov basis for the singular partof the Brauer semigroup, Turkish J. Math. (2018) (To be published).

[2] L. A. Bokut, G. Kukin, Algorithmic and Combinatorial Algebra, Kluwer, Dor-drecht, 1994.

[3] L. A. Bokut, Y. Chen, Grobner-Shirshov bases: some new results, Proceedings ofthe 2nd International Congress of Algebras and Combinatorics, World Scientific,2008, 35-56.

[4] L. A. Bokut, Y. Chen, K. P. Shum, Some new results on Grobner-Shirshov bases,Proceedings of the International Conference on Algebra, Indonesia, 2010.

[5] L. A. Bokut, P. S. Kolesnikov, Grobner-Shirshov bases: from their incipiency tothe present, J. Math. Sci. 116 (2003), 2894-2916.

[6] B. Buchberger, An algorithm for finding a basis for the residue class ring of azero-dimensional polynomial ideal (in German). PhD, University of Innsbruck,Innsbruck, Austria, 1965.

[7] Y. Chen, J. Qiu, Grobner-Shirshov basis of Chinese monoid, J. Algebra Appl. 7(2008), 623-628.

[8] H. Hironaka, Resolution of singularities of an algebraic variety over a field ofcharacteristic zero I, II, Ann. Math. 79 (1964), 109-203, 205-326.



[9] A. I. Shirshov, Certain algorithmic problem for Lie algebras, Sibirskii Math Z. 3(1962), 292-296 (in Russian); English translation in SIGSAM Bull. 33 (1999), 3-6.

aDepartment of Mathematics, Faculty of Art and Science, Balikesir

University, Cagis Campus, Balikesir, 10145, Turkey.

bDepartment of Mathematics, Faculty of Science, King Abdulaziz Uni-

versity, Jeddah, 21589, Saudi Arabia.

cDepartment of Mathematics, Kamil Ozdag Science Faculty, Karamanoglu

Mehmetbey University, Yunus Emre Campus, Karaman, 70100, Turkey.

E-mail : [email protected], [email protected],[email protected]



Multiple zeta values at the non-positive

integers

Boualem Sadaouia

Abstract

In this talk, we relate the special value at a non positive integer s = (s1, ..., sn) =−N = (−N1, ...,−Nn) obtained by meromorphic continuation of the multiplezeta function

Z(s) =∑

m∈N∗n

n∏i=1

1

(m1 + · · ·+mi)si

to special values of the function

Y (s) =

∫[1,+∞[n

n∏i=1

1

(x1 + · · ·+ xi)sidx.

for this, we use Raabe’s formula and the Bernoulli numbers.

2010 Mathematics Subject Classifications : 11M32, 11M41Keywords: Multiple zeta function; integral representation; multiple zeta values.

References

[1] S. Akiyama and S. Egami and Y. Tanigawa, Analytic continuation of multiplezeta-functions and their values at non-positive integers, Acta Arith., 98,2, 107–116,2001.

[2] E. Friedman and S. Ruijsenaars, Shintani-Barnes zeta and gamma functions, Ad-vances Math. 187, 362–395, 2004.

[3] L. Guo and B. Zhang, Renormalization of multiple zeta values,J. Alge-bra,319,9,2008.

[4] D. Manchon and S. Paycha,Nested sums of symbols and renormalised multiplezeta functions, Int. Math. Res. Not.,24,4628-4697,2010.

[5] B. Sadaoui, Multiple zeta values at the non-positive integers, Comptes RendusMathematique, 352, 12, 977-984, 2014.

[6] D. Zagier, Values of zeta functions and their applications, First European Congressof Mathematics (Paris, 1992),Vol. II,A. Joseph et. al.(eds), Birkhauser, Basel, 497-512,1994.

aLaboratory Lesi, University of Khemis Miliana, Route Theniet El-

had 44225, Algeria.




Classical character of 2-OPS

Ali Krelifa1

Abstract

In this paper we study the classical character of 2-OPS whose generatingfunction satisfies a first order differential equation. Our results give some infor-mation about the classical character of the 2-Sheffer-Meixner type polynomials.

2010 Mathematics Subject Classifications : 33C45, 42C05Keywords: Orthogonal polynomials, d-Orthogonal polynomials, Classical poly-

nomials, hypergeometric function

References

[1] N. Asai, I. Kubo, H. -H. Kuo, Multiplicative renormalization and generating func-tions II, Taiwanese J. Math. 8 (2004), 593-628

[2] N. Asai, I. Kubo, H. -H. Kuo, The Brenke type generating functions and explicitforms of MRM triples by means of q-hypergeometric functions, Infin. Dimens.Anal. Quantum. Probab. Relat. Top. 16, (2013), 1350010-1-17

[3] Y. Ben Cheikh and N. Ben Romdhane, d-orthogonal polynomial sets of Chebyshevtype, in: S. Elaydi, et al. (Eds.), Proceeding of the International Conferenceon Difference Equations, Special Functions and orthogonal Polynomials, Munich,Germany, 25-30 July 2005, World Scientific, 2005, pp. 100-111.

[4] Y. Ben Cheikh and N. Ben Romdhane, On d-symmetric classical d-orthogonalpolynomials, J. Comput. Appl. Math. 236 (2011) 85-93.

[5] Y. Ben Cheikh and N. Ben Romdhane, On d-symmetric d-orthogonal polynomialsof Brenke type, J. Math. Anal. Appl. 416 (2014) 735-747.

[6] Y. Ben Cheikh, K. Douak, On the classical d-orthogonal polynomials defined bycertain generating functions, II, Bull. Belg. Math. Soc. 8 (2001) 591-605.

[7] Y. Ben Cheikh and A. Zeghouani, Some discrete d-orthogonal polynomial sets, J.Comp. Appl. Math. 156 (2003) 2-22.

[8] Y. Ben Cheikh and A. Zeghouani, d-orthogonality via generating functions, J.Comp. Appl. Math. 199 (2007) 253-263.

[9] A. Boukhemis, P. Maroni, Une caracterisation des polyn omes strictement 1/porthogonaux de type Scheffer. Etude du cas p=2, J. Approx. Theory 54 (1988),67-91.

[10] A. Boukhemis, A study of a sequence of classical orthogonal polynomials ofdimension 2, J. Approx. Theory 90 (1997), 435-454.

[11] A. Boukhemis, On the classical 2-orthogonal polynomials sequences of sheffer-Meixner type, Cubo. A Math. J. 7 (2005), 39-55.



[12] T. S. Chihara, An Introduction to Orthogonal Polynomials , Gordon and Breach,New York, 1978.

[13] P. Maroni, J. Van Iseghem, Generating functions and semi-classical orthogonalpolynomials, Proc. Roy. Soc. Edinburgh Sect. A 124 (1994), no. 5, 1003-1011.

[14] J. Meixner, Orthogonale polynomsysteme mit einer besonderen gestalt der erzeu-genden funcktion, J. London Math. Soc. 9 (1934), 6-13.

1Department of Mathematics,University of Khemis Miliana, Road of

Theniet El-Had, Khemis Miliana, 44225 Algeria

E-mail : [email protected], [email protected]



On the Truncation Error in the Solution of

Dirichlet Problem for Laplace’s Equation

in Plane by Finite Differences Using

Hexagonal Grid

Suzan C. Buranaya

Abstract

We give the estimation of truncation error in the solution of Dirichlet problemfor Laplace’s equation in a plane by using hexagonal grid under the assumptionthat the boundary function possesses a bounded fifth derivative. By using dis-crete Fourier analytic method, the bound obtained is order of O

(h4

), where

h is the length of the hexagon along x-axis and depends on the bounds of thefifth derivatives of the boundary functions only. Theoretical results are justifiedwith numerical examples.

2010 Mathematics Subject Classifications : 65N06,65N15,65N22,65N99Keywords: Laplace’s equation, Dirichlet boundary value problem, Hexagonal

grid, truncation error.

References

[1] W. Wasow, On the truncation Error in the Solution of Laplace’s Equation byFinite Differences, Journal of Research of the National Bureau of Standards., Vol.48, No. 4, (1952) p. 345-348.

[2] A.A. Dosiyev, E. Celiker, Approximation on the hexagonal grid of the Dirichletproblem for Laplace’s equation, Boundary Value Problems, (2014), 2014:73.

aDepartment of Mathematics, Faculty of Arts and Sciences, Eastern

Mediterranean University, Famagusta, North Cyprus, Via Mersin 10,

Turkey.




One D(4)-Diophantine triples of Fibonacci

numbers.

Salah Eddine Rihane a, Mohand Ouamar Hernaneb, Alain Togbe c

Abstract

Let Fm be themth Fibonacci number. In this talk, we prove that if F2n+6Fk+4 and 4F2n+4Fk + 4 are both perfect squares, then k = 2n for n ≥ 1, exceptwhen n = 1 case in which we can additionally have k = 1.

2010 Mathematics Subject Classifications : 11D09, 11D45, 11B37, 11J86.Keywords: Diophantinem-tuples, Fibonacci numbers, linear form in logarithms.

References

[1] L. Bacic and A. Filipin, The extensibility ofD(4)-pairs, Math. Commun. 18 (2013),447–456.

[2] A. Filipin, B. He, A. Togbe, On the D(4)-triple {F2k, F2k+6, 4F2k+4}, FibonacciQuart. 48.3 (2010), 219–227.

[3] B. He, F. Luca, A. Togbe, Diophantine triples of Fibonacci numbers, Acta Arith-metica. 175 (2016), 57–70.

a bFaculty of Mathematics, University of Sciences and Technology

Houari-Boumediene (USTHB), BP. 32, 16111 Bab-Ezzouar Algiers, Al-

geria

cDepartment of Mathematics, Statistics, and Computer Science, Pur-

due University Northwest, 1401 S, U.S. 421, Westville IN 46391, USA.

E-mail : [email protected], mhernane.usthb.dz, [email protected]



Numerical solution of a free surface flow

problem over an obstacle

Dahbia Hernane a, Samira Beyoud b

Abstract

In this work, we consider a free surface flow problem of an incompressibleand inviscid fluid, perturbed by a topography placed on the bottom of a chan-nel. We suppose that the flow is steady, bidimensional and irrotational. Weneglect the effects of the superficial tension but we take into account of thegravity acceleration g. The main unknown of our problem is the equilibrum freesurface of the flow; its determination is based on the Bernoulli equation whichis transformed as the forced Korteweg-de Vries equation. The problem is solvednumerically via the fourth-order Runge Kutta method for the subcritical case,and the finite difference method for the supercritical case.

2010 Mathematics Subject Classifications : 35R35, 76B07, 76B45Keywords: Free surface problem, Subcritical flow, Supercritical flow, Froude

number.

References

[1] M. B. Abd-el-Malek, Super-critical free-surface flow over a trapezoidal obstacle,Journal of Computational and Applied Mathematics. 66 (1996), 279–291.

[2] L. K. Forbes and L. W. Schwartz, Free-surface flow over a semicircular obstruction,J. Fluid Mech. 114 (1982), 299–314.

[3] J. Marc and V. Broeck, Free surface flow over an obstruction in a channel, Phys.Fluids. 30 (1987), 2315–2317.

a bFaculty of Mathematics, University of Sciences and Technology

Houari-Boumediene (USTHB), BP. 32, 16111 Bab-Ezzouar Algiers, Alge-

ria




Multiple orthogonal polynomials on the

semicircle

Marija P. Stanica

Abstract

In this talk two types of multiple orthogonal polynomials on the semicirclewith respect to a set of r different weight functions are considered. Such poly-nomials are generalizations of polynomials orthogonal on the semicircle withrespect to a complex–valued inner product [f, g] =

∫ π

0f(eiθ

)g(eiθ

)w(eiθ

)dθ.

We present proof of the existence and uniqueness of such multiple orthogonalpolynomials for certain classes of weight functions. Also, some properties ofmultiple orthogonal polynomials on the semicircle including certain recurrencerelations of order r+ 1 are presented. Finally, an application in numerical inte-gration is given.

2010 Mathematics Subject Classifications : 42C05, 33C47, 65D32Keywords: Polynomials orthogonal on the semicircle, Multiple orthogonality,

Recurrence relations, Optimal set of quadrature rules.

aDepartment of Mathematics and Informatics, Faculty of Science,

University of Kragujevac, Kragujevac, Serbia




On The Partially q-Poly-Euler Polynomial

of The Second Kind

Veli Kurta

Abstract

In this work, we define the partially q-poly-Euler polynomials of the sec-ond kind. We have some basic properties of this polynomials such as addition,alternative finite sum and symmetry property. We also give some relations be-tween the partially q-poly-Euler polynomials of the second kind and q-Bernoullipolynomials Bn,q(x, y).

2010 Mathematics Subject Classifications : 11B65, 11B75, 33B10Keywords: Euler numbers and polynomials, q-Euler polynomials of second kind,

polylogarithms functions, q-Stirling numbers of the second kinds.

References

[1] R. P. Agarwal, Y. Y. Kang and C. S. Ryoo, A new q-Extension of Euler polyno-mials of the second kind and some related polynomials, J. Comp. Anal. and App.27(1) (2019), 136-148.

[2] Y. Hamahata, Poly-Euler polynomials and Arakava-Kaneko type zeta functions,Functione et App. Commentarii Math., 51(1) (2014), 7-27.

[3] V. Kurt, Some identities and recurrence relations for the q-Bernoulli and q-Eulerpolynomials, Hacettepe J. of Math. and Statistics, 44(16), (2015), 1397-1404.

[4] N. I. Mahmudov, q-Analogue of the Bernoulli and Genocchi polynomials and theSrivastava-Pinter addition theorem, Disc. Dyn. in Nat. and Soc., (2012), ArticleID: 169348.

[5] C. S. Ryoo and R. P. Agarwal, Some identities involving q-poly-Tangent numbersand polynomials and distribution of their zeros, Adv. in Diff., (2017), 2017.213.

aAntalya TR-07058, Turkey.




Notes On The Poly-Korobov Type

Polynomials and Related Polynomials

Burak Kurta

Abstract

In this article, we consider and investigate the poly-Changhee polynomialsand poly-Korobov type Changhee polynomials and the poly-Korobov polyno-mials. We give some explicit relations and identities between these polynomialsand Bernoulli polynomials, Euler numbers and the Stirling numbers of the sec-ond kind. Furthermore, we give some relations for the degenerate Korobov typeChanghee polynomials.

2010 Mathematics Subject Classifications : 11B68, 11B83, 05A19, 26C05Keywords: Euler numbers and polynomials, Bernoulli numbers and polynomials,

The first kind Korobov polynomials, Korobov type Changhee polynomials, Stirlingnumbers of the second kinds.

References

[1] A. Bayad and Y. Hamahata, Polylogarithms and poly-Bernoulli polynomials,Kyus. J. Math., (2011), 15-24.

[2] Y. Hamahata, Poly-Euler polynomials and Arakava-Kaneko type zeta functions,Functione et App. Commentarii Math., 51(1) (2014), 7-27.

[3] D. S. Kim and T. Kim, Some identities of Korobov type polynomials associatedwith p-adic integers on Zp, Adv. in Diff. Equa., (2015), 2015.282.

[4] J. J. Seo and T. Kim, Degenerate Korobov polynomials, App. Math. Sci., 10(4),(2016), 167-173.

[5] A. Yardımcı and Y. Simsek, Identities for Korobov-type polynomials arasing fromfunctional equations and p-adic integrals, J. of Nonlinear Sci. and App., 10 (2017),2767-2777.

aAkdeniz University, Mathematics of Department, Antalya TR-07058,

Turkey.




Multiple orthogonal trigonometric

polynomials of semi-integer degree and the

corresponding quadrature rules

Gradimir V. Milovanovica, Marija P. Stanicb, Tatjana V. Tomovicb

Abstract

In this paper we consider evaluation of a set of p ∈ N definite integrals re-lated to a common integrand over the same interval E of length 2π, but takenwith respect to the different weight functions. For that purpose we consider anoptimal set of quadrature rules with an odd number of nodes for trigonometricpolynomials in the sense of Borges [Numer. Math. 67 (1994), 271–288]. Theoptimal set of quadrature rules is characterized by multiple orthogonal trigono-metric polynomials of semi–integer degree. We give main properties of suchmultiple orthogonal trigonometric system as well as the numerical procedurefor constructing the corresponding quadrature rules. Theoretical results areillustrated by some numerical examples.

2010 Mathematics Subject Classifications : 42C05, 65D32Keywords: Multiple orthogonal trigonometric polynomials, recurrence relations,

optimal set of quadrature rules

References

[1] C. F. Borges, Ona class of Gausslike quadrature rules, Numer. Math. 67 (1994),271–288.

[2] G. V. Milovanovic, M. P. Stanic, T. V. Tomovic, Trigonometric multiple orthogo-nal polynomials of semiinteger degree and the corresponding quadrature formulas,Publ. Inst. Math. (Beograd) (N. S.) 96(110) (2014), 211-226.

[3] M. P. Stanic, T. V. Tomovic, Multiple orthogonality in the space of trigonometricpolynomials of semi-integer degree, FILOMAT 29(10) (2015), 2227–2237.

aSerbian Academy of Sciences and Arts, Belgrade, Serbia.

bFaculty of Science, University of Kragujevac, Kragujevac, Serbia.

E-mail : [email protected], [email protected], [email protected]



Tensors and the Clifford Algebra: Special

case Pinched Tensor Product

Yousuf Alkhezi

Abstract

The purpose of this paper is to examine general properties of the Tensorsand the Clifford Algebra: Special case Pinched Tensor Product. These proper-ties are compared to the analogue ordinary ones. The importance of this studycomes from the fact that the special case pinched tensor product has not muchbeen researched. The method is to replace the ordinary tensor product withthe Pinched tensor product. Also, in this paper we examine general propertiesof the pinched tensor product. These properties are compared to the analogueordinary ones. The study is extended to elaborate the reciprocity.

Mathematics subject classification: (2010) 15A66, 11E88, 20B25, 47A80.

Keywords: Clifford algebra, Geometric Algebra, Lie algebras, Tensor product,Pinched tensor product.

Acknowledgment

The author is grateful to Public Authority for Applied Education and Trainingfor supporting this research project No BE-17-22. Also, we are indebted to ProfessorM. ABUBAKAR HAGI for assistance in preparing the figures.

References

[1] Y. Benhadid, Y. Alkhezi. Clifford geometric algebra and compact wavelet support.International Mathematical Forum, Vol. 12, 2017, no. 11, 515-525.

[2] L. W. Christensen, D. A. Jorgensen, Tate (co)homology via pinched complexes.Trans. Amer. Math. Soc. 366, 2014, no. 2, 667-689.

[3] Y. Alkhezi. General properties of a morphism on the Pinched tensor product overassociative rings. Submitted.

[4] J. Rotman. An introduction to homological algebra. Second edition. Universitext.Springer, New York, 2009.

[5] A. Weibel. An introduction to homological algebra. Cambridge Studies in Ad-vanced Mathematics, 38. Cambridge University Press, Cambridge, 1994.

[6] A. Charlier, F. Daniele, A. Berard, and M. Charlier. Tensors and the Cliffordalgebra: Application to the physics of bosons and fermions, 1992.

[7] P. Lounesto. Clifford algebras and spinors. Vol. 286. Cambridge university press,2001.



Public Authority for Applied Education and Training

College of Basic Education Mathematics Department Kuwait




Efficient optimal families of higher-order

iterative methods with local convergence

Ramandeep Behla , Jose Manuel Gutierrezb , I. K. Argyrosc , Ali Saleh Alshomrania

Abstract

The main aim of this manuscript is to propose two new schemes havingthree and four substeps of order eight and sixteen, respectively. Both families areoptimal in the sense to Kung-Traub conjecture. The derivation of them are basedon the weight function approach. In addition, theoretical and computationalproperties are fully investigated along with two main theorems describing theorder of convergence. Further, we also provide the local convergence of them inBanach space setting under weak conditions. From the numerical experiments,we find that they perform better than the existing ones when we checked theperformance of them on a concrete variety of nonlinear scalar equations. Finally,we analyze the complex dynamical behavior of them which also provide a greatextent to this.

2010 Mathematics Subject Classifications : 65G99, 65H10, 47J25,Keywords: Nonlinear equations, Convergence analysis, Newton’s method, Basin

of attraction, Banach space

References

[1] J.F. Traub, Iterative methods for the solution of equations, Prentice- Hall Seriesin Automatic Computation (1964) (Englewood Cliffs, NJ)

[2] A. A. Magrenan, I.K. Argyros, A contemporary study of iterative methods: con-vergence, dynamics and applications, Elsevier 2018

[3] Babajee, D.K.R., Cordero, A., Torregrosa, J.R. Study of iterative methodsthrough the Cayley Quadratic Test. J. Comput. Appl. Math. 2016; 291: 358-369.

[4] M.S. Petkovıc, B. Neta, L. Petkovıc, J. Dzunic, Multipoint methods for solvingnonlinear equations, (2013) (Elsevier)

aDepartment of Mathematics, King Abdulaziz University, Jeddah 21577,

Saudi Arabia

bInstitute of Physics of Cantabria (CSIC – University of Cantabria),

39005, Spain

cCameron University, Department of Mathematics Sciences Lawton,

OK 73505, USA

E-mail : [email protected], [email protected], [email protected], [email protected]



Numerical Solution of Ordinary

Differential Equations and Burger-Huxley

Second Order Partial Differential

Equations using Splines

Abdallah Rababah1

Abstract

Ordinary and Partial Differential Equations ( ODEs and PDEs) are widelyused to model and describe many real-life problems. The non-linear PDEsdescribe many models in the various fields of engineering and science like fluiddynamics, diffusion, wave, heat, elasticity, potential, stochastic, and quantummechanics. The solutions of these equations are handled either analytically ornumerically by constructing efficient methods and algorithms. In modeling theinteraction between reaction mechanisms, diffusion transports, and convectioneffects arise the socalled Burger-Huxley equations; besides their use to modelnonlinear phenomenas in engineering and applied mathematics such as wallmotion in liquid crystals and to describe the turbulance in one-dimensionalspace. Numerical solutions and methods are in many applications and situationspreferable.

Piecewise polynomial approximations became recently the most powerfulmethods used in engineering and science applications to offer solutions to chal-lenging issues. B-splines are the proper bases to satisfy the smoothness con-ditions at the break points and matching curves. The parameter interval isdivided into subintervals at the knot sequence. The Bezier curves posses veryinteresting properties like recurrence relation, simplicity of generating points,direct differentiation, simple integration, known formula of degree raising, andmany other favourable properties.

There are several techniques used in solving the Burger-Huxley equation likeAdomian method, homotopy analysis method, tanh-coth method, quadraturetechnique method, homotopy perturbation method, finite-difference method,and B-spline quasi-interpolation method. Many existing numerical methodsto solve Burger-Huxley equations require solving ill-conditioned linear systemsof equations.

In this talk, our aim is to develop numerical algorithms based on the useof splines and their derivatives without requiring the solution of the resultingsystem that might be ill-conditioned. The algorithm will be applied to initialvalue-boundary value problems; in particular, proper technique is aimed to beimproved for the Burger-Huxley equations. It is anticipated that the approxi-mate solution of the IV-BV problems has significant accuracy and efficiency.

1Department of Mathematical Sciences, United Arab Emirates Uni-

versity, Al Ain, UAE




A family of higher-order iteration functions

for the solutions of nonlinear models

Ramandeep Behla, I.K. Argyrosb, Ali Saleh Alshormania, Samaher Khalaf Alharbia

Abstract

Many real life problems can be reduced to scalar and vectorial nonlinearequations by using mathematical modelling. In this paper, we introduce a newfamily of sixth-order iterative for obtaining the solution of scalar equations.Then, we expand the applicability of the same family to the multidimensionalcase preserving the same convergence order. We also analysis the theoreticalconvergence properties of them in both cases. In addition, we present the com-putable radii for the guaranteed convergence of them in Banach space settingand error bounds based on the Lipschitz constants. Moreover, we shown theapplicability of them on some real life problems e.g. Continuous stirred tankreactor (CSTR), kinematic syntheses, chemical engineering, Bratus 2D, Fish-ers, boundary value and Hammerstein integral problems. Finally, we concludebecause of obtained numerical experiments that they perform better in termsof residual error, error between the two consecutive iterations, asymptotic errorconstant term and approximated root as contrast to the earlier iterative methodsof same order in scalar as well as multidimensional case.

2010 Mathematics Subject Classifications : 65G99, 65H10, 47J25,Keywords: Nonlinear systems, Newton’s method, iterative methods, Banach

space, Computational order of convergence.

References

[1] J.F. Traub, Iterative methods for the solution of equations, Prentice- Hall Seriesin Automatic Computation (1964) (Englewood Cliffs, NJ)

[2] I.K. Argyros, Convergence and Application of Newton-type Iterations, (2008)(Springer)

[3] M.S. Petkovıc, B. Neta, L. Petkovıc, J. Dzunic, Multipoint methods for solvingnonlinear equations, (2013) (Elsevier)

aDepartment of Mathematics, King Abdulaziz University, Jeddah 21577,

Saudi Arabia

bCameron University, Department of Mathematics Sciences Lawton,

OK 73505, USA

E-mail : [email protected], [email protected], [email protected],[email protected]



On the ω−Multiple Meixner Polynomials of

First Kind

Sonuc Zorlu Ogurlua , Ilkay Elidemirb

Abstract

In this study, we introduce a new family of discrete multiple orthogonalpolynomial, namely ω−multilple Meixner polynomial, where ω is real number.Some structural properties such as raising operator, Rodrigue’s type formula,generating function and explicit representations are derived. It is also provedthat when ω = 1, the obtained results coincide with the existing results formultiple Meixner polynomials.

2010 Mathematics Subject Classifications : 33E50, 42C05, 33B15Keywords: Multiple orthogonal polynomials, ω-multilple Meixner polynomials,

Rodrigue’s formula, generating function.

References

[1] A.I.Aptekarev, Multiple orthogonal polynomials, J.Comput.Appl.Math. 99 (1998)423–447.

[2] J. Arvesu, J. Coussement, W. Van Assche, Some discrete multiple orthogonalpolynomials, J.Comput.Appl.Math. 153 (2003) 19-45.

[3] A.Erdelyi, Higher Transcendental Functions, Vol.I, McGraw-Hill Book Company,New York, 1953.

[4] R.Koekoek, R.F.Swarttouw, The Askey-scheme of hypergeometric orthogonalpolynomials and its q-analogue, Reports of the faculty of Technical Mathematicsand Informatics No.98-17, Delft, 1998 (math.CA/[email protected]).

[5] S. Mubeen, A. Rehman, A Note on k−Gamma Function and Pochhammerk−Symbol, J.Informatics and Math. Sciences, 6 (2014) 93-107.

[6] A.F. Nikiforov, S.K. Suslov, V.B. Uvarov, Classical Orthogonal Polynomials of aDiscrete Variable, Springer, Berlin, 1991.

[7] W.Van Assche, E.Coussement, Some classical multiple orthogonal polynomials,J.Comput.Appl.Math.127 (2001) 317–347.

aDepartment of Mathematics, Faculty of Arts and Science Univer-

sity of Eastern Mediterranean, Famagusta , Cyprus.

bDepartment of Mathematics, Faculty of Arts and Science Univer-

sity of Eastern Mediterranean, Famagusta , Cyprus.

E-mail : [email protected] , [email protected]



On the ω−Multiple Charlier Polynomials

Mehmet Ali Ozarslana , Gizem Baranb

Abstract

In this study, we introduce a new family of discrete multiple orthogonalpolynomial, namely ω−multilple Charlier polynomial, where ω is real number.Some structural properties such as raisig operator, Rodrigue’s type formula,generating function and explicit representations are derived. It is also provedthat when ω = 1, the obtained results coincide with the existing results formultiple Charlier polynomials.

2010 Mathematics Subject Classifications : 33C45, 33D50, 33E50, 42C05.Keywords: Multiple orthogonal polynomials, ω-multilple Charlier polynomials,

hypergeometric function, Rodrigue’s formula, generating function.

References

[1] A.I.Aptekarev, Multiple orthogonal polynomials, J.Comput.Appl.Math. 99 (1998)423–447.

[2] J. Arvesu, J. Coussement, W. Van Assche, Some discrete multiple orthogonalpolynomials, J.Comput.Appl.Math. 153 (2003) 19-45.

[3] A.Erdelyi, Higher Transcendental Functions, Vol.I, McGraw-Hill Book Company,New York, 1953.

[4] R.Koekoek, R.F.Swarttouw, The Askey-scheme of hypergeometric orthogonalpolynomials and its q-analogue, Reports of the faculty of Technical Mathematicsand Informatics No.98-17, Delft, 1998 (math.CA/[email protected]).

[5] S. Mubeen, A. Rehman, A Note on k−Gamma Function and Pochhammerk−Symbol, J.Informatics and Math. Sciences, 6 (2014) 93-107.

[6] A.F. Nikiforov, S.K. Suslov, V.B. Uvarov, Classical Orthogonal Polynomials of aDiscrete Variable, Springer, Berlin, 1991.

[7] W.Van Assche, E.Coussement, Some classical multiple orthogonal polynomials,J.Comput.Appl.Math.127 (2001) 317–347.

aDepartment of Mathematics, Faculty of Arts and Science Univer-

sity of Eastern Mediterranean, Famagusta, Cyprus.

bDepartment of Mathematics, Faculty of Arts and Science Univer-

sity of Eastern Mediterranean, Famagusta, Cyprus.




Domination on hyperbolic graphs

Rosalıo Reyesa , Jose M. Rodrıgueza , Jose M. Sigarretab,c , Marıa Villetad

Abstract

Let G = (V,E) be a finite connected graph and S ⊆ V . S is a distancek-dominating set if every vertex v ∈ V is within distance k from some vertexof S. S is a total dominating set if every vertex v ∈ V satisfies δS(v) ≥ 1.The minimum cardinals among all distance k-dominating sets of G and all totaldominating sets of G are the distance k-domination number, γk

w(G), and thetotal domination number, γt(G), respectively. The study of hyperbolic graphsis an interesting topic since the hyperbolicity of any geodesic metric space isequivalent to the hyperbolicity of a graph related to it. In this paper we obtainrelationships between the hyperbolicity constant δ(G) and some dominationparameters of a graph G, such as γk

w(G) ≥ 2δ(G)/(2k+1) and δ(G) ≤ γt(G)/2+3.

2010 Mathematics Subject Classifications : 05C07, 92E10.Keywords: Graphs; domination theory; total domination; Gromov hyperbolic-

ity.

Acknowledgements

This work was supported in part by four grants from Ministerio de Economıa yCompetititvidad, Agencia Estatal de Investigacion (AEI) and Fondo Europeo de De-sarrollo Regional (FEDER) (MTM2016-78227-C2-1-P and MTM2017-90584-REDT),Spain.

References

[1] J. Alonso, T. Brady, D. Cooper, T. Delzant, V. Ferlini, M. Lustig, M. Mihalik,M. Shapiro and H. Short, Notes on word hyperbolic groups, in: E. Ghys, A. Hae-fliger, A. Verjovsky (Eds.), Group Theory from a Geometrical Viewpoint, WorldScientific, Singapore, 1992.

[2] C. Berge, Theory of graphs and its applications, Methuen, London, 1962.

[3] S. Bermudo, J. M. Rodrıguez and J. M. Sigarreta, Computing the hyperbolicityconstant, Comput. Math. Appl. 62 (2011), 4592–4595.

[4] B. H. Bowditch, Notes on Gromov’s hyperbolicity criterion for path-metric spacesin Group theory from a geometrical viewpoint, Trieste, 1990 (ed. E. Ghys, A.Haefliger and A. Verjovsky; World Scientific, River Edge, NJ, 1991) 64–167.

[5] E. J. Cockayne, B. Gamble and B. Shepherd, An upper bound for the k-dominationnumber of a graph, J. Graph Theory 9(4) (1985), 533–534.



[6] E. Delavina, R. Pepper and B. Waller, Lower bounds for the domination number,Discus. Math. Graph Theory 30 (2010) 475–487.

[7] H. Fernau, J. A. Rodrıguez-Velazquez and J. M. Sigarreta, Global powerful r-alliances and total k-domination in graphs, Utilitas Math. 98 (2015), 127–147.

[8] Ghys, E. and de la Harpe, P., Sur les Groupes Hyperboliques d’apres MikhaelGromov. Progress in Mathematics 83, Birkhauser Boston Inc., Boston, MA, 1990.

[9] M. Gromov, Hyperbolic groups, in Essays in group theory. Edited by S. M. Ger-sten, M. S. R. I. Publ. 8. Springer, 1987, 75–263.

[10] O. Ore, Theory of Graphs, A. M. S. Colloquium Publications 38 (1962), 270pages.

[11] M. Soto, Quelques proprietes topologiques des graphes et applications a Internetet aux reseaux, Ph. D. Thesis. Universite Paris Diderot - Paris VII, 2011.

aDepartamento de Matematicas, Escuela Politecnica Superior, Uni-

versidad Carlos III de Madrid, Avenida de la Universidad 30, 28911

Leganes (Madrid), Spain.

bFacultad de Matematicas, Universidad Autonoma de Guerrero, Car-

los E. Adame No.54 Col. Garita, 39650 Acalpulco Gro., Mexico.

cInstituto de Fısica, Benemerita Universidad Autonoma de Puebla,

Apartado Postal J-48, Puebla 72570, Mexico.

dDepartamento de Estadıstica e Investigacion Operativa III, Facul-

tad de Estudios Estadısticos, Universidad Complutense de Madrid, Av.

Puerta de Hierro s/n., 28040 Madrid, Spain.

E-mail : [email protected], [email protected], [email protected],[email protected]



Structure theorem for quasihyperbolic

metric

Jesus Gonzaloa, Ana Portillab, Jose M. Rodrıguezc, Eva Tourısa

Abstract

It is known that complete Riemannian surfaces can be obtained by gluingfour kind of pieces. In this paper we prove an analogue result in the context ofplane domains with their quasihyperbolic metric.

2010 Mathematics Subject Classifications : 53C20, 53C22, 53C23.Keywords: Quasihyperbolic metric, geodesics, closed geodesics, plane domains,

Riemannian surfaces, decomposition of surfaces.

Acknowledgements

This work was supported in part by four grants from Ministerio de Economıa yCompetititvidad, Agencia Estatal de Investigacion (AEI) and Fondo Europeo de De-sarrollo Regional (FEDER) (MTM2013-46374-P, MTM2016-78227-C2-1-P, MTM2015-69323-REDT and MTM2017-90584-REDT), Spain.

References

[1] Alvarez, V., Rodrıguez, J. M., Structure theorems for Riemann and topologicalsurfaces, J. London Math. Soc. 69 (2004), 153–168.

[2] Fernandez, J. L., Melian, M. V., Escaping geodesics of Riemannian surfaces, ActaMath. 187 (2001), 213–236.

[3] Gehring, F. W., Osgood, B. G., Uniform domains and the quasi-hyperbolic metric,J. Anal. Math. 36 (1979), 50–74.

[4] Gehring, F. W., Palka, B. P., Quasiconformally homogeneous domains, J. Anal.Math. 30 (1976), 172–199.

[5] Martin, G. J., Quasiconformal and bi-Lipschitz homeomorphisms, uniform do-mains and the quasihyperbolic metric, Trans. Amer. Math. Soc. 292 (1985), 169–191.

[6] Massey, W. M., Algebraic Topology: An Introduction. Harcourt, Brace and World,Inc., New York, 1967.

[7] Melian, M. V., Rodrıguez, J. M., Tourıs, E., Escaping geodesics in Riemanniansurfaces with pinched negative curvature. Submitted.

[8] Portilla, A., Rodrıguez, J. M., Tourıs, E., Structure theorem for Riemanniansurfaces with arbitrary curvature, Math. Z. 271 (2012), 45–62.



[9] Vaisala, J., Quasihyperbolic geometry of planar domains, Ann. Acad. Sci. Fenn.34 (2009), 447–473.

aDepartamento de Matematicas, Facultad de Ciencias, Universidad

Autonoma de Madrid, Campus Cantoblanco, Ctra. Colmenar, Km.15,

28049 Madrid, Spain.

bSt. Louis University (Madrid Campus), Math. Department, Avenida

del Valle 34, 28003 Madrid, Spain.

cDepartamento de Matematicas, Universidad Carlos III de Madrid,

Avenida de la Universidad 30, 28911 Leganes (Madrid), Spain.




On the factorisation of p-adic meromorphic

functions; primality and pseudo-primality

Zerzaihi Tahara, Boutabaa Abdelbakib, Saoudi Bilalc

Abstract

In this talk, we study primality and pseudo-primality of p-adic meromorphicfunctions and the property of left(resp.right) primeness of these functions . Wealso consider the probleme of permutability of entire p-adic functions

2010 Mathematics Subject Classifications : 30D05, 30D35Keywords: permutability, right primeness, left primeness, p-adic meromorphic

functions.

References

[1] J.P. Bezevin and A. Boutabaa, Decomposition of p-adic meromorphic functions,Ann.Math.Blaise Pascal, vol.2 N1, 1995 , 51-60.

[2] Y.Noda, On the entire functions. KodaiMath.J.4(1981), 480-494.

[3] A. Escassut, Analytic eements in p-adic Analysis, World Scientific Publishing,Singapoure, 1995.

aDepartment of Mathematics, Faculty of Science and informatics,

University of Mohamed Seddik Ben Yahia, Jijel 18000, Algeria.

E-mail : [email protected] of Mathematics, Faculty of science, University of Cler-

mont Auvergne, ClermontFerrand 63178

E-mail : [email protected] of Mathematics, Faculty of Science and informatics,

University of Mohamed Seddik Ben Yahia, Jijel 18000, Algeria.




Relations of the geometric-arithmetic

index with some topological indices

Ana Granadosa, Ana Portillaa, Jose M. Rodriguezb, Jose M. Sigarretac

Abstract

Although the concept of geometric-arithmetic index has been introduced inthe chemical graph theory recently, it has already proved to be useful. Theobjective of this paper is twofold: First, to obtain new relations connecting thegeometric-arithmetic index with other topological indices; second, to character-ize graphs which are extremal with respect to them.

2010 Mathematics Subject Classifications : 05C07, 92E10.Keywords: Geometric-arithmetic index, Vertex-degree-based topological index,

variable Zagreb index.

Acknowledgements

This work was supported in part by two grants from Ministerio de Economıa yCompetitividad, Agencia Estatal de Investigacin (AEI) and Fondo Europeo de De-sarrollo Regional (FEDER) (MTM2016-78227-C2-1-P and MTM2017-90584-REDT),Spain.

References

[1] K. C. Das, On geometric-arithmetic index of graphs, MATCH Commun. Math.Comput. Chem. 64 (2010), 619–630.

[2] K. C. Das, I. Gutman, B. Furtula, On first geometric-arithmetic index of graphs,Discrete Appl. Math. 159 (2011), 2030–2037.

[3] K. C. Das, I. Gutman, B. Furtula, Survey on Geometric-Arithmetic Indices ofGraphs, MATCH Commun. Math. Comput. Chem. 65 (2011), 595–644.

[4] I. Gutman, Degree–based topological indices, Croat. Chem. Acta 86 (2013), 351–361.

[5] I. Gutman, K. C. Das, The first Zagreb index 30 years after, MATCH Commun.Math. Comput. Chem. 50 (2004), 83–92.

[6] I. Gutman, T. Reti, Zagreb group indices and beyond, Int. J. Chem. Model. 6:2-3 (2014), 191–200.

[7] I. Gutman, N. Trinajstic, Graph theory and molecular orbitals. Total π-electronenergy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535–538.



[8] X. Li, J. Zheng, A unified approach to the extremal trees for different indices,MATCH Commun. Math. Comput. Chem. 54 (2005), 195–208.

[9] A. Milicevic, S. Nikolic, On variable Zagreb indices, Croat. Chem. Acta 77 (2004),97–101.

[10] M. Randic, Novel graph theoretical approach to heteroatoms in QSAR, Chemo-metrics Intel. Lab. Syst. 10 (1991), 213–227.

[11] M. Randic, On computation of optimal parameters for multivariate analysis ofstructure-property relationship, J. Chem. Inf. Comput. Sci. 31 (1991), 970–980.

[12] M. Randic, D. Plavsic, N. Lers, Variable connectivity index for cycle-containingstructures, J. Chem. Inf. Comput. Sci. 41 (2001), 657–662.

[13] TRC Thermodynamic Tables. Hydrocarbons; Thermodynamic Research Center,The Texas A & M University System: College Station TX; 1987.

[14] M. Voge, A. J. Guttmann, I. Jensen, On the number of benzenoid hydrocarbons,J. Chem. Inf. Comput. Sci. 42 (2002), 456–466.

[15] D. Vukicevic, B. Furtula, Topological index based on the ratios of geometricaland arithmetical means of end-vertex degrees of edges, J. Math. Chem. 46 (2009),1369–1376.

[16] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem.Soc. 69 (1947), 17–20.

[17] B. Zhou, N. Trinajstic, On general sum-connectivity index, J. Math. Chem. 47(2010), 210–218.

aSt. Louis University (Madrid Campus)

Math. Department, Avenida del Valle 34, 28003 Madrid, Spain.

bDepartamento de Matematicas, Escuela Politecnica Superior, Uni-

versidad Carlos III de Madrid, Avenida de la Universidad 30, 28911

Leganes (Madrid), Spain.

cFacultad de Matematicas, Universidad Autonoma de Guerrero, Car-

los E. Adame No.54 Col. Garita, 39650 Acalpulco Gro., Mexico




On Double Rotations in Minkowski

Space-time

Melek Erdogdua, Mustafa Ozdemirb

Abstract

A rotation with two plane of rotations is a double rotation. The rotation canbe said to take place in both planes of rotation. These planes are orthogonal. Adouble rotation has two angles of rotation, one for each plane of rotation. Therotation is specified by giving the two planes and two non-zero angles. This studyis concern with generating the double rotations in Minkowski space-time by usingsemi skew symmetric matrices. For this purpose, we use the decomposition ofa semi skew-symmetric matrix A = θ1A1 + θ2A2 by two unique semi skew-symmetric matrices A1 and A2 satisfying the properties A1A2 = 0, A3

1 = A1

and A32 = −A2. By using this decomposition of semi skew-symmetric matrices,

we give two different methods to generating rotation matrices with semi skew-symmetric matrices in E4

1. One of them is called Rodrigues rotation formulaand the other one is called Cayley rotation formula. The explicit form of therotation matrices, which are generated by these formulas, are obtained. If θ1, θ2are nonzero and θ1 �= θ2, then formulas generate double rotations. On the otherhand, we give way of finding the skew-symmetric matrix, which generates a givendouble rotation matrix by Rodrigues and Cayley rotation formulas, separately.

2010 Mathematics Subject Classifications : 15B10, 15A16, 53B30.Keywords: Minkowski Space-time, Rotation Matrix, Cayley Formula, Rodrigues

Formula.

References

[1] M. Ozdemir and A.A. Ergin, Rotations with unit timelike quaternions inMinkowski 3-space, Journal of Geometry and Physics. 56 (2006), 322-336.

[2] J. H. Gallier, Notes on Differential Geometry and Lie Groups. University ofPennsylvania; 2014.

[3] C. M. Geyer, Catadioptric Projective Geometry: Theory and Applications. Doc-torial Dissertation, University of Pennsylvania (2003).

[4] T. Politi, A Formula for the Exponential of a Real Skew-Symmetric Matrix ofOrder 4, BIT Numerical Mathematics. 41 (2001), 842-845.

[5] J. Gallier and D. Xu, Computing Exponentials of Skew Symmetric Matricesand Logarithms of Orthogonal Matrices, International Journal of Robotics andAutomation. 18 (2000), 10-20.

[6] L. Kula, M. K. Karacan and Y. Yaylı, Formulas for the Exponential of SemiSymmetric Matrix of order 4, Mathematical and Computational Applications.10 (2005), 99-104.



[7] J. E. Mebius, Derivation of Euler-Rodrigues Formula for three-dimansional rota-tions from the general formula for four dimensional rotations, arxiv: math.GM(2007).

[8] S. Ozkaldı and H. Gundogan, Cayley Formula, Euler Parameters and Rotationsin 3- Dimensional Lorentzian Space, Advances in Applied Clifford Algebras. 10(2010), 367-377.

[9] A. N. Norris, Euler-Rodrigues and Cayley Formulae for Rotation of ElasticityTensors, Mathematics and Mechanics of Solids. 13 (2008), 465-498.

[10] D. Serre, Matrices: Theory and Applications, Graduate text in Mathematics,Springer - Verlag, London; 2002.

aDepartment of Mathematics-Computer Sciences, Faculty of Science

Necmettin Erbakan University, Konya TR-42090, Turkey.

E-mail : [email protected] of Mathematics, Faculty of Science University of Akd-

eniz, Antalya TR-07058, Turkey.




Generalized Darboux Frame of Curves on

Hypersurfaces in Euclidean Four Space

Melek Erdogdua

Abstract

In this study, generalization of Darboux frame of curves in Euclidean 4-space is investigated. Firstly, the curvature functions kn, kg, τg, τn, σn, σg of(α,M) curve-hypersurface couple are defined. Then the relations between Frenetand Darboux frame are stated. Moreover, curvature functions of (α,M) curve-hypersurface couple are given in terms of curvature functions κ, τ and σ ofthe curve α. And some results are stated on special curves ( asymptotic curves,geodesic curves and line of curvature) of hypersurfaces. In addition, some specialcases are examined. It is explained that how to find one of the Darboux frameand its curvature functions for these cases. Finally, some discussions have beenmade on the obtained results. Actually, it is seen that this construction is thegeneralization of from Darboux frame in Euclidean 3-space to Euclidean 4-space.

2010 Mathematics Subject Classifications : 14Q05, 53A04, 14J70.Keywords: Euclidean 4-space, Darboux Frame.

References

[1] B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity. AcademicPress Inc., London, 1983.

[2] H. Gluck, Higher curvatures in Euclidean space, American Mathematical monthly,1966,73, 699-704.

[3] M. Duldul, B.U. Duldul, N. Kuruoglu, E. Ozdamar, Extention of Darboux frameinto Euclidean 4-space and its invariants, Turkish journal of Mathematics, 2017,41, 1628-1639.

[4] I. Kisi, M. Tosun, Spinor Darboux Equations of Curves in Euclidean 3-Space,2015,Mathematica Moravica, 19-1, 87–93.

[5] O.Bektas, S. Yuce, Special Smarandache Curves According to Darboux Frame inE3, Romanian Journal of Mathematics and Computer Sciences, 2013, 3-1, 48-59.

[6] B. Altunkaya and F.K. Aksoyak, Curves of Constant Breadth According to Dar-boux Frame, Commun.Fac.Sci.Univ.Ank.Series A1, 2017, 66, 44–52.

[7] N. Macit, M. Duldul, Some new associated curves of a Frenet curve in E3 and E4,Turkish Journal of Mathematics, 2014, 38: 1023 -1037.

[8] M.P. Do Carmo, Differential geometry of curves and surfaces, USA, Printice Hall,1976.

[9] J. Oprea, Differential geometry and its applications, Cleveland State University,Printice Hall, 1997.



aDepartment of Mathematics-Computer Sciences, Faculty of Science

Necmettin Erbakan University, Konya TR-42090, Turkey.




Weak Solutions for Nonlinear Fractional

Differential Equations in Banach Spaces

Fatima Zohra Mostefaia , Mouffak Benchohrab

Abstract

This note is concerned with the existence of solutions of the boundary valueproblem with fractional order differential equations with mixed boundary con-ditions of the form

cDαx(t) = f(t, x(t)), for each t ∈ I = [0, T ], (1)

x(0) + μ

∫ T

0

x(s)ds = x(T ), (2)

where cDα, 0 < α ≤ 1 is the Caputo fractional derivative. Our results are basedon the technique of measures of weak noncompactness and a fixed point theoremof Monch type.

2010 Mathematics Subject Classifications : 26A33, 34B15, 34G20Keywords: Caputo fractional derivative, measure of weak noncompactness, Pet-

tis integrals.

References

[1] A. Amrani, C. Castaing and M. Valadier, Convergence in Pettis norm under ex-treme point condition, Vietnam Journal of Mathematics., (4), 323-335 (1998).

[2] M. Benchohra, J.R. Graef, F. Mostefai, Weak solutions for nonlinear fractionaldifferential equations on reflexive Banach spaces, Electron. J. Qual. Theory Differ.Equ. 54 (2010), 1-10.

[3] M. Benchohra, J. Graef and F-Z. Mostefai, Weak solutions for boundary-valueproblems with nonlinear fractional differential inclusions, Nonlinear Dynamics andSystem Theory 11 (3) (2011), 227-237.

aLaboratory of Mathematics Geometry, Analysis, Control and Ap-

plications, Tahar Moulay University of Saida, Algeria.

bLaboratory of Mathematics, Sidi Bel-Abbes University, Algeria




On the Taketa inequality

Burcu Cınarcıa, Temha Erkocb

Abstract

1A well-known conjecture about the character degrees of a finite solvablegroup G is known as the Taketa inequality i.e. dl(G) ≤ |cd(G)| where dl(G) isthe derived length of G and cd(G) is the set of all irreducible complex characterdegrees of G. This inequality has been conjectured by G. Seitz and I. M. Isaacs.Although this conjecture is still open, in the literature we know that some classesof solvable groups satisfy the Taketa inequality. For example, this inequality istrue for all M -groups [3] and for all finite groups of odd order [2].Now let χ be an irreducible complex character of G. The product χχ is also acharacter of G where χ is the complex conjugate character of χ. In this talk weinvestigate the relationship between the decomposition of the character χχ intoits distinct irreducible constituents and the Taketa inequality.

2010 Mathematics Subject Classifications : 05A10, 05A15, 11B68, 11S80,26C05, 65D17

Keywords: Solvable groups, Derived length and the Taketa inequality.

References

[1] E. Adan-Bante, Products of characters and derived length, J. Algebra, 266 (2003),305-319.

[2] T. R. Berger, Characters and Derived Length in Groups of Odd Order, J. Algebra,39 (1976), 199-207.

[3] I. M. Isaacs, Character Theory of Finite Groups, Academic Press, New York, 1976.

[4] M. L. Lewis, Derived lengths and character degrees , Proc. Amer. Math. Soc.,126(7) (1998), 1915-1921.

aPiri Reis University, Maritime Faculty, 34940, Istanbul, Turkey

bIstanbul University, Faculty of Science, Department of Mathemat-

ics, 34134 Istanbul,Turkey


1The work of the authors was supported by Scientific Research Projects Coordination Unit ofIstanbul University. The project number is 27148.



Anti–synchronization of nonidentical

fractional order hyperchaotic systems

Abedel-Karrem Alomaria

Abstract

Chaos anti–synchronization between fractional order hyperchaotic Lorenzand Chen system is theoretically and numerically studied. The suitable condi-tions for achieving anti–synchronization of these fractional differential systemsare given. Numerical simulations coincide with the theoretical analysis are in-troduced.

2010 Mathematics Subject Classifications : 93A30, 93D15 , 37N35Keywords: Active control; Anti–synchronization; Fractional hyperchaotic Lorenz

system; Fractional hyperchaotic Chen system.

References

[1] H. Zhu, S. Zhou, Z. He, Chaos synchronization of the fractional-order Chenssystem, Chaos, Solitons & Fractals 41 (2009),2733–7.

[2] C. Li, G. Peng, Chaos in Chens system with a fractional order, Chaos, Solitons &Fractals22 (2004),443-7.

[3] K. Diethelm,. An algorithm for the numerical solution of differential equations offractional order. Elec. Trans. Numer. Anal. 5 (1997),1-6.

[4] I.Podlubny, Fractional differential equations, Academic Press, New.

aDepartment of Mathematics, Faculty of Science, Yarmouk Univer-

sity, 211-63 Irbid, Jordan.




Slightly ω − (μ, σ)-irresolute functions

between generalized topological spaces

Samer Al Ghour1 , Abeer Al-Nimer2

Abstract

Slightly ω-(μ, σ)-irresolute functions are introduced and investigated in thestructure of generalized topological spaces. Several characterizations, implica-tions and examples related to this concept are introduced.

2010 Mathematics Subject Classifications : 54C10.

References

[1] S. Al Ghour and W. Zareer, Omega open sets in generalized topological spaces.J. Nonlinear Sci. Appl. 9 (2016), no. 5, 3010–3017.

[2] A. Al-Omari and T. Noiri, A unified theory of contra-(μ, λ)-continuous functionsin generalized topological spaces. Acta Math. Hungar. 2012; 135(1-2): 31–41.

[3] A. Csaszar, Generalized topology, generalized continuity. Acta Math. Hungar. 96(2002), no. 4, 351–357.

[4] A. Csaszar, γ-connected sets, Acta Math. Hungar., 2003; 101, 273–279.

[5] A. Csaszar, Extermally disconnected generalized topologies, Ann. Univ. Sci. Bu-dapest. Eotvos Sect. Math., 2004; 47: 91–96.

[6] A. Csaszar, Products of generalized topologies, Acta Math. Hungar., 2009; 123:127–132.

[7] D. Jayanthi, Contra continuity on generalized topological spaces. Acta Math.Hungar. 2012; 137(4): 263–271.

[8] Y. K. Kim and W. K. Min, On operations induced by hereditary classes ongeneralized topological spaces. Acta Math. Hungar. 2012; 137(1-2): 130–138.

[9] Y. K. Kim and W. K. Min, R (g, g′)-continuity on generalized topological spaces.Commun. Korean Math. Soc. 2012; 27(4): 809–813.

[10] E. Korczak-Kubiak, A. Loranty and R. J. Pawlak, Baire generalized topologicalspaces, generalized metric spaces and infinite games. Acta Math. Hungar. 2013;140(3): 203–231.

[11] V. Renukadevi and P. Vimaladevi, Note on generalized topological spaces withhereditary classes. Bol. Soc. Parana. Mat. (3) 2014; 32(1): 89–97.

1Department of Mathematics and Statistics, Jordan University of

Science and Technology

2Department of Mathematics and Statistics, Jordan University of

Science and Technology




Approximation of fixed points of nonlinear

contractions in metric space

Petko D. Proinova

Abstract

Let (X, d) be a complete (dislocated) metric space and T : X → X be amapping satisfying the following contractive condition:

ψ(d(Tx, Ty)) ≤ ϕ(d(x, y)) for allx, y ∈ X with d(Tx, Ty) > 0,

for some functions ψ,ϕ : (0,∞) → R. In this talk, we present sufficient condi-tions for the functions ψ and ϕ which ensure that T has a unique fixed pointin X and the sequence (Tnx) of successive approximations is convergent to thisfixed point. The main result generalizes and extends the classical theorem ofBoyd and Wong [1] as well as recent results of Jleli and Samet [2], Wardowski[3, 4] and others.

2010 Mathematics Subject Classifications : 47H10, 54H25Keywords: Fixed points, Nonlinear contractions, Metric spaces.

Acknowledgement

This work was supported by the National Science Fund of the Bulgarian Ministryof Education and Science under contract DN 12/12 of 20.12.2017.

References

[1] D. W. Boyd, J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc.20 (1969) 458–464, doi:10.1090/S0002-9939-1969-0239559-9.

[2] M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J.Inequal. Appl. 2014:38 (2014) 1–8, doi: 10.1186/1029-242X-2014-38

[3] D. Wardowski, Fixed points of a new type of contractive mappings in completemetric spaces, Fixed Point Theory Appl. 2012:94 (2012) 1–6, doi:10.1186/1687-1812-2012-94.

[4] D. Wardowski, Solving existence problems via F -contractions, Proc. Amer. Math.Soc. 146 (2018) 1585–1598, doi:10.1090/proc/13808.

aFaculty of Mathematics and Informatics, University of Plovdiv Paisii

Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria.




On the Partially q-Poly-Bernoulli Numbers

and Polynomials

Secil Bilgic1, Veli Kurt2

Abstract

In last ten years, many mathematicians studied q-Bernoulli polynomials andq-Euler polynomials. Mahmudov introduced and investigated Bernoulli poly-nomials Bn,q (x, y) and q-Genocchi polynomials Gn,q (x, y). Kurt gave someidentities and relations for these polynomials.

In this work, we define generated partially q-Bernoulli polynomialsB[k,α]n,q (x, y)

of order α. We give new relation between the partially q-Poly-Bernoulli polyno-mials B

[k,α]n,q (x, y) of order α and the q-Poly-Genocchi polynomials G

[k,α]n,q (x, y)

of order α. Stirling numbers of the second kind S2,q (n, k).

2010 Mathematics Subject Classifications : 11B75,11B83.Keywords: Bernoulli numbers and polynomials, Euler numbers and polynomi-

als, Genocchi numbers and polynomials, q-Bernoulli polynomials, q-Euler polynomi-als, q-Genocchi polynomials, Polylogarithm function, Stirling numbers of the secondkind, Poly-Bernoulli polyinomials, Poly-Genocchi polinomials, the 2-variable Hermite-Kampe de Feriet polynomials.

References

[1] A. Bayad and Y. Hamahata, Polylogarithm and poly-Bernoulli polynomials,Kyushu J. Math. 65 (2011), 15–34.

[2] J. L. Cieslinski, Improved q-exponential and q-trigonometric functions. AppliedMath. Letters 24 (2011), 2110–2114.

[3] U. Duran, M. Acikgoz, S. Arac, Unified (p, q)-analogue of Apostol type polyno-mials of order, Filomat 32(2) (2018), 387–394.

[4] V. Kurt, New identities and relations derived from the generalized Bernoulli poly-nomial, Euler and Genocchi polynomials. Advanced in Diff. Equ. 2014, 2014.5(2014).

[5] N. I. Mahmudov, q-Analoques of the Bernoulli and Genocchi polinomials and theSrivastava-Pinter addition theorem, Discrete Dyn. Nat. Soc., Article. ID.169.348(2012).

1Istanbul Aydin University, ABMYO Bilg. Prog(UE), Istanbul, Turkey.

2Department of Mathematics, Faculty of Science University of Akd-

eniz TR-07058 Antalya, Turkey




Some operator inequalities and their

applications

Hamdullah Basaran1 , Mehmet Gurdal2 , Aysenur Guncan3

Abstract

We prove analogs of certain operator inequalities, including Holder-McCarthyinequality, Kantorovich inequality and Heinz-Kato inequality, for positive oper-ators on the Hilbert space in terms of Berezin symbols and Berezin number ofoperators on the reproducing kernel Hilbert space.

2010 Mathematics Subject Classifications : 47A63, 26D15, 47B10Keywords: Reproducing kernel Hilbert space, Berezin symbol, Berezin num-

ber, positive operator, Holder-McCarthy type inequality, Kantorovich type inequality,Heinz-Kato inequality

Acknowledgements

This paper was supported by SDU BAP Project FYL-2018-6700.

References

[1] N. Altwaijry, A. S. Baazeem, M. Garayev, Distance estimates, norm of Hankeloperators and related questions, Operators and Matrices, 12(1)(2018), 157–168.

[2] N. Aronzajn, Theory of reproducing kernels, Trans. Amer. Math. Soc., 68(1950),337–404.

[3] F. A. Berezin, Covariant and contravariant symbols for operators, Math. USSR-Izv., 6(1972), 1117–1151.

[4] T. Furuta, Invitation to Linear Operators, From Matrices to bounded linear op-erators on a Hilbert space, Taylor & Francis, London and New York, 255 pp.,2001.

[5] M. T. Garayev, Berezin symbols, Holder-McCarthy and Young inequalities andtheir applications, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 43(2)(2017),287–295.

[6] M. T. Garayev, M. Gurdal, S. Saltan, Hardy type inequality for reproducing kernelHilbert space operators and related problems, Positivity, 21(4)(2017), 1615–1623.

[7] M. Gurdal, U. Yamancı, M. Garayev, Some results for operators on a model space,Frontiers of Mathematics in China, 13(2)(2018), 287–300.

[8] U. Yamancı, M. Gurdal, M. T. Garayev, Berezin number inequality for convexfunction in Reproducing Kernel Hilbert Space, Filomat, 31(18)(2017), 5711–5717.



1Department of Mathematics, Suleyman Demirel University, 32260,

Isparta, Turkey


Isparta, Turkey


Isparta, Turkey




Advanced refinements of Hilbert-type

inequalities in a difference form

Mario Krnic1 , Tserendorj Batbold2 , Josip Pecaric3

Abstract

In this talk we establish several more accurate Hilbert-type inequalities ina difference form. Our main results rely on some recent improvements of theYoung inequality. First, we give refinements and reverses of the Holder inequal-ity. Then, by virtue of the improved Holder inequality, we give two classes ofrefinements and reverses for general Hilbert-type inequalities. As an application,we give strengthened forms of the classical Hilbert and Hardy inequalities.

2010 Mathematics Subject Classifications : 26D10, 26D15Keywords: Hilbert inequality, Hardy inequality, Young inequality, Holder in-

equality, refinement

References

[1] T. Batbold, M. Krnic, J. Pecaric, More accurate Hilbert-type inequalities in adifference form, Results. Math. (2018) 73:121 https://doi.org/10.1007/s00025-018-0885-7.

[2] D. Choi, M. Krnic, J. Pecaric, Improved Jensen-type inequalities via linear inter-polation and applications, J. Math. Inequal. 11 (2017), 301–322.

[3] G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, second edition, CambridgeUniversity Press, Cambridge, 1967.

[4] M. Krnic, J. Pecaric, General Hilbert’s and Hardy’s inequalities, Math. Inequal.Appl. 8 (2005), 29–52.

1University of Zagreb, Faculty of Electrical Engineering and Com-

puting, Unska 3, 10000 Zagreb, Croatia

2Department of Mathematics & Institute of Mathematics, National

University of Mongolia, P.O. Box 46A/104, Ulaanbaatar 14201, Mongo-

lia

3University of Zagreb, Faculty of Textile Technology, Prilaz baruna

Filipovica 28a, 10000 Zagreb, Croatia




Orthogonal polynomials and the mismatch

theorem

Stefano Pozza1 , Miroslav Pranic2 , Zdenek Strakos3

Abstract

The main message of the mismatch theorem [2, Theorem 4.1] is that whenincurable breakdown in the Lanczos algorithm occurs, then the spectrum of thecomputed matrix is a subset of the spectrum of the input matrix. In this talk wepresent how the mismatch theorem can be proved using results from [1] aboutorthogonal polynomials with respect to an arbitrary linear functional.

2010 Mathematics Subject Classifications : 65F10, 33C47.Keywords: Linear functionals, Formal orthogonal polynomials, Lanczos algo-

rithm.

References

[1] A. Draux, Polynomes orthogonaux formels - Applications, Lecture Notes in Math-ematics, Vol. 974, Springer-Verlag, Berlin, Heidelberg, New York; 1983.

[2] D. R. Taylor, Analysis of the look ahead Lanczos algorithm, Ph.D. thesis, Centerfor Pure and Applied Mathematics, University of California, Berkeley, CA; 1982.

1Faculty of Mathematics and Physics, Charles University, Prague

2Faculty of Science, University of Banja Luka

3Faculty of Mathematics and Physics, Charles University, Prague

E-mail : [email protected], [email protected],[email protected]



A Generalization of the Suborbital Graphs

Generating Fibonacci Numbers for the

Subgroup Γ3

Seda Ozturk

Abstract

Modular group is one of the most well-known discrete group with manyapplications. This work investigates some subgraphs of the subgroup Γ3 of themodular group Γ defined by

{( a bc d ) ∈ Γ : ab+ cd ≡ 0 (mod 3)}

In previous study mentioned in [1], the subgraph F1,1 of the subgroup Γ3 isonly studied, and Fibonacci numbers are obtained by the subgraph F1,1. In thispaper, we give a generalization of the subgraphs generating Fibonacci numbersfor the subgroup Γ3 and some subgraphs providing special conditions.

2010 Mathematics Subject Classifications : 05C25,11B39Keywords: Modular group, Graph theory, Fibonacci numbers

References

[1] Akbas M.,Kor T. and Kesicioglu, Y. Disconnectedness of the subgraph F 3 for thegroup Γ3, Journal of Inequalities and Applications, 2013.

[2] G. A. Jones, D. Singerman, and K. Wicks, The Modular Group and General-ized Farey Graphs, London Mathematical Society Lecture Note Series, CambridgeUniversity Press, 160, 1991.

[3] Rankin, R.A., Modular Forms and Functions,Cambridge University Press, Cam-bridge, 2008.

Department of Mathematics, Avrasya University




New asymptotic expansions and

approximation formulas for the factorial

function

Tomislav Buric1

Abstract

Well-known Stirling approximation for the factorial function

n! ≈√2πn

(n

e

)n

is one of the most beautiful formulas in mathematics. This is in fact a shorteningof the asymptotic expansion for the gamma function which was also studied inother similar forms by Laplace, De Moivre, Ramanujan, Wehmeier and recentlyby Karatsuba, Gosper, Batir, Mortici, Nemes and others.

But all this formulas have been considered separately and connection betweenthem was not clear. Moreover, the compution of each term in this formulaswas a tedious job without any attempt to find general procedure to calculatecoefficients in this type of asymptotic expansions.

In this talk we present general expansion for the gamma function introducingparameter m. Using properties of asymptotic power series, we proved asymp-totic expansion for the factorial function

n! ∼√2πn

(n

e

)n[ ∞∑k=0

Pk n−k

]1/m

,

where coefficients (Pn) satisfy simple recursive algorithm.This allows easy calcuation of the coefficients in all of the previously men-

tioned expansions and leads to various other generalizations and improvementsof the approximation formulas for the gamma function and related classicalfunctions.

2010 Mathematics Subject Classifications : 41A60, 33B15Keywords: Gamma function, Factorial Function, Asymptotic expansion

1University of Zagreb, Faculty of Electrical Engineering and Com-

puting




Addition Behavior of an Arf Numerical

SemigroupNesrin Tutas1 , Nihal Gumusbas2

Abstract

The aim of this work is to exhibit some combinatorial behaviors of Arf semi-groups.

2010 Mathematics Subject Classifications : 20M14, 05A17Keywords: Arf numerical semigroup, Young diagram

References

[1] C. Arf, Une interpretation algebrique de la suite ordres de multiplicite d’unebranche algebrique, Proc London Math Soc. 20 (1949), 256-287.

[2] V. Barucci, D.E. Dobbs and M. Fontana, Maximality properties in numerical semi-groups and applications to one-dimensional analytically irreducible local domains,Mem. Am. Math. Soc. 125 (1997), 598, 1-77.

[3] M. Bras-Amoros, A. Mier, Representation of numerical semigroups by Dyck paths,Semigroup Forum. 75 (2007), 676-681.

[4] H. Constantin , B. Houston-Edwards, N. Kaplan, Numerical sets, core partitions,and integer points in polytopes, Combinatorial and Additive Number Theory II–CANT, New York, NY, USA, 2015 and 2016, Springer Proc. Math. Stat., 220 (2017), 99-127.

[5] W. Fulton, Young Tableaux, With Application to Representation Theory andGeometry, New York: Cambridge Univ Press; 1997.

[6] P.A. Garcia-Sanchez, H.I. Karakas, B.A. Heredia, JC. Rosales,Parametrizing Arf numerical semigroups, J. Algebra Appl., 16 (2017).https://doi.org/10.1142/S0219498817502097

[7] H.I. Karakas, Parametrizing numerical semigroups with multiplicity 5, Int. J.Algebr. Comput., 28(2018), 01 , 69-95.

[8] W.J. Keith, R.Nath, Partitions with prescribed hooksets, J. Comb. and Num.Thy., 3 (2011), 1, 39-50.

[9] J.C. Rosales, P.A. Garcia-Sanchez, Numerical Semigroups, New York: Springer;2009.

[10] N. Tutas, H.I. Karakas and N.Gumusbas, Young tableux and Arf partitions,submitted.

1Department of Mathematics, Akdeniz University, Antalya, Turkey

2Department of of Mathematics, Akdeniz University, Antalya




Maximal commutative subalgebras of a

Grassmann algebra

Ho-Hon Leung1 , Victor Bovdi2

Abstract

We provide a new approach to the investigation of maximal commutativesubalgebras (with respect to inclusion) of Grassmann algebras. We show thatfinding a maximal commutative subalgebra in Grassmann algebras is equivalentto constructing an intersecting family of subsets of various odd sizes in [n] whichsatisfies certain combinatorial conditions. Then we find new maximal commu-tative subalgebras in the Grassmann algebra of odd rank n by constructing suchcombinatorial systems for odd n. These constructions provide counterexamplesto conjectures made by Domokos and Zubor in 2015.

References

[1] M. Domokos and M. Zubor, Commutative subalgebras of the Grassmann algebra,J. Algebra Appl. 14(8): 1550125, 13, 2015.

[2] H.-H. Leung (with V. Bovdi), Maximal commutative algebras of a Grassmannalgebra, to appear in J. Algebra Appl.

1United Arab Emirates University

2United Arab Emirates University




Extended incomplete version of

hypergeometric functions

Mehmet Ali Ozarslana , Ceren Ustaoglub

Abstract

Recently, the incomplete Pochhammer ratios are defined in terms of incom-plete beta and gamma functions. In this paper, we introduce the extendedincomplete version of Pochhammer symbols in terms of the generalized incom-plete gamma functions. With the help of these extended incomplete version ofPochhammer symbols we introduce the extended incomplete version of Gausshypergeometric and Appell’s functions and investigate several properties of themsuch as integral representations, derivative formulas, transformation formulas,Mellin transforms and log convex properties. Furthermore, we investigate incom-plete fractional derivatives for extended incomplete version of some elementaryfunctions.

2010 Mathematics Subject Classifications : 33B20, 33C05, 26A33Keywords: incomplete gamma function, incomplete beta function, extended

incomplete version of Pochhammer symbols, extended incomplete version of hyperge-ometric functions, incomplete Riemann-Liouville fractional derivative operators

References

[1] M. A. Ozarslan, C. Ustaoglu, Incomplete Riemann-Liouville fractional derivativeoperators and incomplete hypergeometric functions, Submitted.

[2] M. A. Ozarslan, C. Ustaoglu, Incomplete Caputo fractional derivative operators,https://doi.org/10.1186/s13662-018-1656-1.

[3] H. M. Srivastava, M. Aslam Chaudhry, R. P. Agarwal, The incomplete Pochham-mer symbols and their applications to hypergeometric and related functions, In-tegral Transforms and Special Functions, 23 (2012), 659-683.

[4] M. A. Chaudhry, S. M. Zubair, Extended incomplete gamma functions with ap-plications, J. Math. Anal. Appl., 274 (2002), 725-745.

[5] M. A. Chaudhry, S. M. Zubair, Generalized incomplete gamma functions withapplications, Journal of Computational and Applied Mathematics, 55 (1994), 99-124.

aDepartment of Mathematics, Faculty of Arts and Science, Eastern

Mediterranean University, Gazimagusa, TRNC, Mersin 10, Turkey

bDepartment of Computer Engineering, Faculty of Engineering, Fi-

nal International University, Kyrenia, TRNC, Mersin 10, Turkey




A note on Pointwise Convergence by

Nonlinear Singular Integral Operators in

Mobile Interval

Mine Menekse Yılmaz1

Abstract

The object of this study is deal with the pointwise approximation of thenonlinear integral operators given by

Vλ (x) =

b+λ∫a−λ

Kλ (t− x, f (t)) dt, x ∈ D,

where a and b are any real numbers and D = (a− λ, b+ λ) is mobile interval, atμ-generalized Lebesgue point of integrable function f ∈ Lp (R) , as (x, λ) tends(x0, λ0) . Here Λ is the index set of nonnegative numbers with accumulationpoint λ0, the kernel function Kλ : R×R→ R is Lebesgue integrable on R2 andsatisfies the Lipschitz condition with respect to the second variable in order touse known proof technique used in linear setting.

2010 Mathematics Subject Classifications : 41A35, 41A25,47G10Keywords: pointwise convergence, nonlinear singular integral, μ generalized

Lebesgue point.

References

[1] C. Bardaro, J. Musielak, G. Vinti, Nonlinear integral operators and applications,DeGruyter Series in Nonlinear Analysis and Applications, 9 (2003), xii + 201 pp.

[2] A.D. Gadjiev, On the order of convergence of singular integrals which depend ontwo parameters, Special Problems of Functional Analysis and their Appl. to theTheory of Diff. Eq. and the Theory of Func., Izdat. Akad. Nauk Azerbaıdazan.SSR. (1968), 40–44.

[3] H. S. Jung, N. Deo, M. Dhamija, Pointwise approximation by Bernstein typeoperators in mobile interval, Appl. Math. Comput., 214 (1) (2014), pp. 683–694.

[4] H. Karsli, Convergence and rate of convergence by nonlinear singular integral op-erators depending on two parameters, Applicable Analysis, 85(6-7) (2006), pp.781-791.

[5] J. Musielak, On some approximation problems in modular spaces, In: Proceedingsof Int. Conf. on Constructive Function Theory, Varna 1981, Sofia (1983), pp. 455–461.

[6] B. Rydzewska, Approximation des fonctions par des integrales singulieres ordi-naires, Fasc. Math. 7 (1973), pp. 71–81.



1Gaziantep University, Faculty of Arts and Science, Department of

Mathematics, Gaziantep, 27310, Turkey




Some basic properties of the generalized

bi-periodic Fibonacci and Lucas sequences

Elif Tan1

Abstract

A generalization of Fibonacci sequence is introduced by Yayenie [4] andindependently by Sahin [1] as:

Q0 = 0, Q1 = 1, Qn =

{aQn−1 + cQn−2, if n is evenbQn−1 + dQn−2, if n is odd

, n ≥ 2

where a, b, c, and d are nonzero real numbers. They are emerged as a generaliza-tion of the best known sequences in the literature, such as Fibonacci sequence,k-Fibonacci sequence, Pell sequence, Jacobsthal sequence, etc. Some modifiedversions of the sequence {Qn} have been studied by several authors. For the caseof c = d = 1, the sequence {Qn} reduces to the bi-periodic Fibonacci sequence,and its companion sequence, bi-periodic Lucas sequence, can be obtained bytaking initial conditions 2 and b. The matrix representation for the bi-periodicFibonacci and Lucas sequences was given firstly in [2], and several propertieswere obtained for the even indices terms of this sequence. Then, in [3], a newmatrix identity for the bi-periodic Fibonacci sequence was given as follows:

S :=

(ab ab1 0

)⇒ Sn = (ab)�n

2 �(

bζ(n)qn+1 aζ(n)bqna−ζ(n+1)qn bζ(n)qn−1

),

where {qn} is the bi-periodic Fibonacci sequence and ζ (n) is the parity function.In this study, we derive some basic properties of the generalized bi-periodicFibonacci and Lucas sequences by using matrix approach.

2010 Mathematics Subject Classifications : 11B39Keywords: Fibonacci sequence, Matrix method

References

[1] M. Sahin, The Gelin-Cesaro identity in some conditional sequences, Hacet. J.Math. Stat. 40(6) (2011), 855-861.

[2] E. Tan and A.B. Ekin, Some Identities On Conditional Sequences By Using MatrixMethod, Miskolc Mathematical Notes, 18(1) (2017), 469-477.

[3] E. Tan, On bi-periodic Fibonacci and Lucas numbers by matrix method, ArsCombinatoria 133 (2017), 107-113.

[4] O. Yayenie, A note on generalized Fibonacci sequence, Appl. Math. Comput. 217(2011), 5603-5611.

1Department of Mathematics, Ankara University




Jungck Type Fixed Point Results in

Rectangular Soft Metric Space

Simge Oztunc1 , Ali Mutlu2 , Sedat Aslan3

Abstract

The aim of this work is to investigate and to present the proof of some com-mon fixed point theorems by using commuting maps in rectangular soft metricspaces. firstly we recall some basic notions of rectangular soft metric space andBanach Contraction Theorem for rectangular soft metric spaces. Afterwards weobtain some common fixed point result by using rectangular soft metric andscaler valued parametric functions.

2010 Mathematics Subject Classifications : 03E72,47H10,54H25Keywords: Soft Rectangular Metric, Common Fixed Points, Weakly Compatible

Mappings

References

[1] S. Banach, Sur les operations dans les ensembles abstraits et leur application auxequa- tions integrales. Fund Math. 3, 133181 (1922)

[2] A.Branciari, A Fixed Point Theorem of Banach-Caccioppoli Type on a Class ofGeneralized Metric Spaces, Publ. Math. Debrecen, Vol: 57, 2000, pp. 31-37.

[3] S.Das, S.K.Samanta, Soft Metric, Annals of Fuzzy Mathematics and InformaticsVolume: 6, No. 1, 2013, pp. 77-94.

[4] H.S.Ding, M.Imdad, S.Radenovi, J.Vujakovi, On some fixed point results in b-metric, rectangular and b-rectangular metric spaces, Arab Journal MathematicalScience 22, 2016, 151164

[5] R. George,R.Rajagopalan,Common fixed point results for contractions in rectan-gular metric spaces, Bull. Math. Anal. Appl. 5 (1) (2013) 4452.

[6] H. Hosseinzadeh, Fixed Point Theorems on Soft Metric Spaces, Journal of FixedPoint Theory and Applications, Volume: 19, Issue 2, 2017, pp 16251647.

[7] G.Jungck, Commuting mappings and fixed points. Amer. Math. Monthly, 83(1976), 261263.

[8] G.Jungck, Compatible mappings and fixed points. Internat. J. Math. Math. Sci.9(4) (1986), 771779.

[9] P. K. Maji , R.Biswas and A. R.Roy, Soft Set Theory, Comput. Math. Appl., 45,2003, 555-562.

[10] D.Molodtsov, Soft Set Theory-First Result, Comput. Math. Appl., 37, 1999, 19-31.



[11] A.Mutlu, N.Yolcu, B.Mutlu, Fixed Point Theorems in Pratially Ordered Rect-angular Metric Spaces, British Journal of Mathematics and Computer Science15(2):1-9,2016.

[12] S.Oztunc, A.Mutlu, S.Aslan, Soft Fixed Point Theorems for Rectangular SoftMetric Spaces, 2. International Students Science Conference, 4-5 May 2018,Izmir/Turkey.

1Department of Mathematics, Manisa Celal Bayar University






Relatively-normal Slant Helices and Their

Characterizations

Nesibe Macit1, Mustafa Duldul1

Abstract

In this study, we define a new curve on an oriented surface by using theDarboux frame {T, V, U} along the curve. This new curve whose vector field Vmakes a constant angle with a fixed direction is called as relatively-normal slanthelix. The axis and some characterizations of such curves are studied. Moreoverwe give some relations between some special curves and relatively-normal slanthelices.

1Department of Mathematics, Yildiz Technical University




On entropies and some special functions

Julije Jaksetic

Abstract

Using maximization of Shannon entropy, under different constraints, we get dif-ferent kind of probability densities from Zipf’s to hybrid Zipf-Mandelbrot andsome others densities spread over positive integers. There is also accompaniedpart, of this approach, with special functions, such as Riemann zeta function,Hurwitz zeta function and Lerch’s transcendent. It turns out that characteriza-tion of analytical properties of the above probability densities leads to, dually,characterization of these special functions. We will characterize, using tech-niques from [1], that all these special functions are exponentially convex, sepa-rately, over all parameters and this fact will enable us to construct various typesof means and lower and upper bounds.

2010 Mathematics Subject Classifications : 26D15, 26D20Keywords: Zipf-Mandelbrot law, Hybrid Zipf-Mandelbrot law, Hurwitz ζ−function,

Lerch’s transcendent, exponentiall convexity

References

[1] J. Jaksetic, J. Pecaric, Exponential Convexity method, J. Convex Anal., 20(1)(2013), 181–197.

[2] J. Jaksetic, D. Pecaric, J. Pecaric,, Some properties of Zipf-Mandelbrot lawand Hurwitz ζ−function, Math. Inequal. Appl. 21 (2) (2018) 575-584.

[3] J. Jaksetic, D. Pecaric, J. Pecaric,, Hybrid Zipf-Mandelbrot law, J. Math.Inequal. (accepted)

Faculty of Food Technology and Biotechnology, University of Za-

greb




On generalized f-divergences through

matrix inequality approach

Dora Pokaz1

Abstract

For a function f : R+ → R and n-tuples of positive real numbers p =(p1, . . . , pn), q = (q1, . . . , qn), I. Csiszar introduced the f -divergence functionalby

Cf (q,p) =

n∑i=1

pif

(qipi

).

In probability theory, an f -divergence is a function Df(P ‖ Q) that measuresthe difference between two probability distributions P and Q. Recently, thereis much interest in those functions because of their applications in probabilitytheory, in information theory, in statistical physics, economics, biology. Firstly,it was customary to assume that function f is a convex. Even Csiszar studiedonly those f -divergences. Later, there were results for other types of functions.Simultaneously, those divergences were generalized mostly by adding a weight.We studied generalized f -divergences for L-Lipschitzian function f .

A real-valued function f : R→ R is called Lipschitz continuous if there existsa positive real constant L such that,

|f(x1)− f(x2)| ≤ L|x1 − x2|,for all x1, x2 ∈ R. The topic is still attractive to the researchers. In this article,stochastic matrix is included in results. Those results are leaning on the Shermaninequality adjusted for L-Lipshitzian functions and applied to generalized f -divergences.

Keywords: L-Lipschitzian function, f -divergence, stochastic matrix

1Faculty of Civil Engineering, University of Zagreb




Some local forms of new convergences and

one type of Arzela Theorem

Doris Doda1 , Agron Tato2

Abstract

Recently, there are many effort to extend the specter of classic convergencesin framework of special topologies of the space under consideration or topologyof image of any class of functions. In this paper we are concern to dependence offorms of some convergences from the neighborhood of the point where happensthis limit process. The well known locally uniformly convergence is a key ofsome applications of this idea and we can reformulate and one type of ArzelaTheorem and find relations of this convergence with quasi-uniformly by segmentsand Alexandroff convergence. Beside above convergence we focus to anotherconvergence which is nearer the alpha-convergence.

Keywords: Local uniformly convergence or δ-convergence, α-convergence, ex-haustive sequence, strong locally uniformly convergence, Alexandroff convergence

References

[1] C. Arzela, Intorno alla continuit della somma di infinita di funzzioni continue,Rend. R. Accad. Sci. Istit. Bologna (1883/1884) 7984

[2] V. Gregoriades, N. Papanastassiou, “The notion of exhaustiveness and Ascoli-typetheorems”

[3] R. Das, N. Papanastassiou, Some types of convergence of sequences of real valuedfunctions, Real Anal. Exchange 28 (2) (2002/2003) 116.

[4] P.S. Alexandroff, Einfhrung in die Mengenlehre und die Theorie der reellen Funk-tionem, Deutsch Verlag Wissenschaft, 1956, translated from the 1948 Russianedition.

[5] R.G. Bartle, On compactness in functional analysis, Trans. Amer. Math. Soc. 79(1955) 3557.

[6] H. Attouch, R. Lucchetti, R. Wets, The topology of the p-Hausdorff distance,Ann. Mat. Pura Appl. 160 (1991), 303320

[7] Kelley, J., General topology, Springer- Verlag, 1975

[8] L. Hola, T. Salat, Graph convergence, uniform, quasi-uniform and continuous con-vergence and some characterizations of compactness, Acta Math. Univ. Comenian.5455 (1998) 121132

[9] Agata Caserta, Giuseppe Di Maio , Lubica Hola, Arzela’s Theorem and stronguniform convergence on bornologies, J. Math. Anal. Appl. 371 (2010) 384392



[10] N. Papanastassiou, On a new type of convergence of sequences of functions,submitted

[11] A. Csaszar and M. Laczkovich, “Discrete and equal convergence”, Studia Sci.Math. Hungar., 10 (1975), 463472.

1Wisdom University

2Department of Mathematics, Faculty of Mathematics and Physics

Engineering, Tirana Polytechnic University




Fuzzy Soft Multi LA-Γ-Semigroups

Canan Akın1

Abstract

In the present paper, multi LA-Γ-semigroups, and also their fuzzy and softextensions are introduced. Some properties of their families for certain opera-tions are investigated. Moreover, a notion of fuzzy multi soft LA-Γ-semigroupis defined as an algebraic extension of fuzzy multi soft sets and some features ofthem are studied.

2010 Mathematics Subject Classifications : 20M10, 20N99, 08A72, 54C60,03E99

Keywords: LA-Γ-Semigroup, Soft Multiset, Fuzzy Soft Multiset

References

[1] A. Aygunoglu and H. Aygun, Introduction to fuzzy soft groups, Computers andMathematics with Applications 58 (2009), 1279–1286.

[2] Y. Celik, C. Ekiz and S. Yamak, A new view on soft rings, Hacettepe Journal ofMathematics and Statistics, 40 (2011), 273–286.

[3] Y. Celik, C. Ekiz and S. Yamak, Applications of fuzzy soft sets in ring theory,Annals of Fuzzy Mathematics and Informatics, 5 (2013) 451–462.

[4] K.P. Girish and S.J. John, General relations between partially ordered multisetsand their chains and antichains, Math. Commun., 14 (2009), 193–206.

[5] A. Kharal and B. Ahmad, Mappings on soft classes, NewMathematics and NaturalComputation, 7 (2011), 471–481.

[6] T. Shah and I. Rehman, On Γ-ideals and Γ-bi-ideals in Γ-AG-groupoids, Interna-tional Journal of Algebra, 4 (2010), no.6, 267–276.

[7] Sk. Nazmul, P. Majumdar and S.K. Samanta, On multisets and multigroups,Annals of Fuzzy Mathematics and Informatics, 6 (2013), 643–656.

[8] Sk. Nazmul and S.K. Samanta, On soft multigroups, Annals of Fuzzy Mathematicsand Informatics, 10 (2015), 271–285.

[9] P.K. Maji and R. Biswas and A.R. Roy, Fuzzy soft sets, J. Fuzzy Math., 9 (2001),589–602.

[10] S. Miamoto, Fuzzy multisets and their generalizations, C.S. Calude et al. (Eds.):Multiset Processing, LNCS 2235, Springer-Verlag Berlin Heidelberg: 2001, pp.225-235.

[11] D. Molodtsov, Soft set theory first results, Computers and Mathematics withApplications, 37 (1999), 19–31.



[12] Q. Mushtaq and S.M. Yusuf, On LA-semigroups, The Alig. Bull. Math., 8(1978),65–70.

[13] D. Pei and D. Miao, From soft sets to information systems, 2005 IEEE Interna-tional Conference on Granular Computing, 2 (2005), 617–621.

[14] S. Sebastian and T.V. Ramakrishnan, Multi-fuzzy sets, International Mathemat-ical Forum, 50 (2010), 2471–2476.

[15] T.K. Shinoj, A. Baby and S.J. John, On some algebraic structures of fuzzymultisets, Annals of Fuzzy Mathematics and Informatics, 9 (2015), 77–90.

[16] Y. Yang, X. Tan, C. Meng, The multi-fuzzy soft set and its application in decisionmaking, Applied Mathematical Modelling, 37 (2013), 4915–4923.

[17] L.A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353.

1Department of Mathematics, Giresun University, 28200, Giresun,

Turkey




On the comparison of two different

one-parametric generalizations of the

logarithmic mean

Mirna Rodic1

Abstract

There exist several generalizations of the well-known logarithmic mean. R.Cisbani, L. Galvani and E. L. Dod independently defined the extended logarith-mic mean Lr. For certain r, this mean becomes the arithmetic mean, geometricmean, logarithmic mean and identric mean, but there is no such r for whichit becomes harmonic mean. On the other hand, H. Alzer defined another one-parametric generalization - the generalized logarithmic mean Fr. For certain r,this mean becomes the arithmetic mean, geometric mean, harmonic mean andlogarithmic mean, but there is no such r for which it becomes identric mean. Inthis talk, it is explained weather these two one-parametric generalizations of thelogarithmic mean are comparable, and how. Their comparison with the powermeans is also given.

2010 Mathematics Subject Classifications : 26E60Keywords: logarithmic mean, extended logarithmic mean, generalized logarith-

mic mean, power mean

1Faculty of Textile Technology, University of Zagreb, Croatia




Lidstone interpolation of composition

function and Steffensen-type inequalities

Asfand Fahad1 , Josip Pecaric2 , Marjan Praljak3

Abstract

We present some new identities and related inequalities by combining theLidstone interpolation with Faa di Bruno’s formula for higher order derivativesof the composition of functions. The obtained results are closely related togeneralizations of Steffensen’s inequality given in [4] and [2].

2010 Mathematics Subject Classifications : 26D10, 26D15Keywords: Steffensen’s inequality, Lidstone interpolation, Faa di Bruno’s for-

mula

References

[1] R. P. Agarwal, P. J. Y. Wong, Error Inequalities in Polynomial Interpolation andTheir Applications, Dordrecht / Boston / London: Kluwer Academic Publishers;1993.

[2] A. Fahad, J. Pecaric, M. Praljak, Generalized Steffensen’s inequality, J. Math.Inequal. 9 (2015), 481–487.

[3] W. P. Johnson, The Curious History of Faa di Bruno’s Formula, Amer. Math.Monthly 109 (2002), 217–234.

[4] J. Pecaric, Connections among some inequalities of Gauss, Steffensen and Os-trowski, Southeast Asian Bull. Math. 13 (1989), 89-91.

1Department of Mathematics, COMSATS Institute of Information

Technology, Vehari, Pakistan

2RUDN University, Miklukho-Maklaya str. 6, 117198 Moscow, Russia

3Faculty Of Food Technology and Biotechnology, University of Za-

greb, Croatia




On Levinson’s inequality involving averages

of 3-convex functions

Ana Vukelic

Abstract

By using the integral arithmetic mean and the Levinson inequality we givethe extension for 3-convex function of Wulbert’s result from [9]. Also, we obtaininequalities with divided differences using the Levinson inequality. As a conse-quence, the convexity of higher order for function define by divided differenceis proved. Further, we construct a new family of exponentially convex functionand Cauchy-type means by exploring at linear functionals with the obtainedinequalities.

2010 Mathematics Subject Classifications : 26D15, 26D07, 26A51, 26B25Keywords: Levinson inequality, divided difference, (n,m)-convexity, exponential

convexity.

References

[1] P. S. Bullen, An inequality of N. Levinson, Univ. Beograd. Publ. Elektrotehn. Fak.Ser. Mat. Fiz. No. 412-460, 109-112.

[2] R. Farwig, D. Zwick, Some divided difference inequalities for n-convex functions,J. Math. Anal. Appl. 108 (1985), 430-437.

[3] S. Karlin, Total Positivity, Stanford Univ. Press, Stanford, 1968.

[4] N. Levinson, Generalization of an inequality of Ky Fan, J. Math. Anal. Appl. 80(1964), 133-134.

[5] J. Pecaric, J. Peric, Improvements of the Giaccardi and the Petrovic inequalityand related Stolarsky type means, An. Univ. Craiova Ser. Mat. Inform. 39 (2012),65–75.

[6] J. E. Pecaric, F. Proschan and Y. L. Tong, Convex functions, partial orderings, andstatistical applications, Mathematics in science and engineering, vol. 187 AcademicPress, 1992.

[7] T. Popoviciu, Sur l’approximation des fonctions convexes d’ordre superieur, Math-ematica 10, (1934), 49-54.

[8] T. Popoviciu, Les functions convexes, Herman and Cie, Editeurs, Paris (1944).

[9] D.E. Wulbert, Favard’s Inequality on Average Values of Convex Functions, Math-ematical and Computer Modelling. 37 (2003), 1383-1391.

Faculty of Food Technology and Biotechnology, University of Za-

greb, Pierottijeva 6, 10000 Zagreb, Croatia




Generalized Block Anti-Gauss Quadrature

Rules

Hessah Alqahtani1 , Lothar Reichel2

Abstract

Golub and Meurant describe how pairs of Gauss and Gauss–Radau quadra-ture rules can be applied to determine inexpensively computable upper andlower bounds for certain real-valued matrix functionals defined by a symmetricmatrix. However, there are many matrix functionals for which their technique isnot guaranteed to furnish upper and lower bounds. In this situation, it may bepossible to determine upper and lower bounds by evaluating pairs of Gauss andanti-Gauss rules. Unfortunately, it is difficult to ascertain whether the valuesdetermined by Gauss and anti-Gauss rules bracket the value of the given real-valued matrix functional. Therefore, generalizations of anti-Gauss rules haverecently been described, such that pairs of Gauss and generalized anti-Gaussrules may determine upper and lower bounds for real-valued matrix functionalsalso when pairs of Gauss and (standard) anti-Gauss rules do not. The avail-able generalization requires the matrix that defines the functional to be real andsymmetric. The present paper extends generalized anti-Gauss rules in severalways: The real-valued matrix functional may be defined by a nonsymmetricmatrix. Moreover, extensions that can be applied to matrix-valued functionsare presented. Estimates of element-wise upper and lower bounds then are de-termined. Finally, modifications that yield simpler formulas are described.

References

[1] T. Kim, q-Volkenborn integration, Russ. J. Math. Phys. 19 (2002), 288–299.

[2] G. G. Lorentz, Bernstein Polynomials, New York: Chelsea Publishing Company;1986.

1Department of Mathematics, Faculty of Science and Arts, King Ab-

dulaziz University, Rabigh, Saudi Arabia

2Department of Second Author, University of Second Department of

Mathematical Sciences, Kent State University, Kent, OH 44242, USA




On Suborbital Graphs and Matrices with

Even Fibonacci and Lucas Numbers

Ummugulsun Akbaba1 , Ali Hikmet Deger2

Abstract

The suborbital graphs are formed by the imprimitive action of the modulargroup Γ on the rational projective line Q := Q ∪ {∞}. In [1] Jones, Singermanand Wicks extend the results of F1,1 Farey graph to suborbital graphs of Fu,N ,where (u,N) = 1 and N > 1.

In [2] A.H. Deger defined the farthest vertices on the paths of minimal lengthon the suborbital graphs and investigated the related continued fractions. Thenexamined the relation between continued fractions and Fibonacci numbers.

In our previous works, we extend the results with Lucas numbers and in thiswork we have given even Fibonacci numbers by using a special transformationwhich gives vertices on the path of minimal length on the suborbital graphs.Then by using matrices which gives relation between continued fractions withFibonacci an Lucas numbers, we have worked characteristic equations for Fi-bonacci and Lucas recurrence relations.

2010 Mathematics Subject Classifications : 11F06, 40A15, 30B70Keywords: Suborbital Graphs, Fibonacci Numbers, Lucas Numbers

References

[1] G.A. Jones, D.Singerman , K. Wicks , The modular group and generalized Fareygraphs, London Math. Soc. Lecture Note Ser., 160, (1991), 316-338.

[2] A.H. Deger, Vertices of paths of minimal lengths on suborbital graphs, Filomat,31 (2017), 913-923.

[3] T.Koshy, Fibonacci and Lucas numbers with applications, A Wiley- IntersciencePublication, Canada, 2001.

[4] A. Cuyt, V.B. Petersen, B. Verdonk, H. Waadeland, W.B. Jones, Handbook ofContinued Fractions for Special Functions, Springer, New York, 2008.

[5] M. Akbas, On suborbital graphs for the modular group, Bull. London Math. Soc.,33, (2001), 647-652.

[6] C.C. Sims, Graphs and finite permutation groups, Math. Zeitschr., 95, (1967),76-86.

[7] A.H. Deger, Relationships with the Fibonacci numbers and the special vertices ofthe suborbital graphs, Gumushane Universitesi Fen Bilimleri Enstitusu Dergisi,7(2017),168-180.



1Institute of Natural Sciences,, Karadeniz Technical University, Tra-

bzon, Turkey

2Department of Mathematics, Karadeniz Technical University, Tra-

bzon, Turkey




Lorentz-Marcinkiewicz Property of Direct

Sum of Operators

Pembe Ipek Al

Abstract

In this paper, the relations between Lorentz-Marcinkiewicz property of thedirect sum of operators in the direct sum of Hilbert spaces and its coordinateoperators are studied.

2010 Mathematics Subject Classifications : 47A05, 47A10, 47A20Keywords: Direct sum of Hilbert spaces and operators, Compact

operator, Lorentz-Marcinkiewicz operator classes

References

[1] A. Pietsch, Operators Ideals, Amsterdam, Holland: North-Holland PublishingCompany; 1980.

[2] J. von Neumann, R. Schatten, The cross-space of linear transformations, Ann.Math. 47 (1946), 608-630.

[3] F. Cobos, D. D. Haroske, T. Khn, T. Ullrich, Mini-workshop: modern applica-tions of s-numbers and operator ideals, Oberwolfach, Germany: MathematischesForschungs Institute Oberwolfach; 8-14 February 2015; 369-397.

[4] F. Cobos, Duality and Lorentz-Marcinkiewicz operator spaces, Math. Scand. 63(1988) 261-267.

[5] H. Triebel, ber die verteilung der approximationszahlen kompakter operatoren inSobolev-Besov-Raumen, Inventiones Mathematicae 4 (1967), 275-293.

Institute of Natural Sciences,, Karadeniz Technical University, Tra-

bzon, Turkey




Star Saturation Number of Random

Graphs

B. Tayfeh-Rezaie

Abstract

Fix a positive integer n and a graph F . A graph G is called F -saturatedif G contains no subgraph isomorphic to F but each graph obtained from Gby joining a pair of non-adjacent vertices contains at least one copy of F as asubgraph. In other words, G is F -saturated if and only if it is an edge-maximalF -free graph. The saturation function of F , denoted sat(n, F ), is the minimumnumber of edges in an F -saturated graph on n vertices.

For a given graph G, a spanning subgraph H of G is said to be an F -saturated subgraph of G if H contains no subgraph isomorphic to F but eachgraph obtained by adding an edge from E(G) \ E(H) to H has at least onecopy of F as a subgraph. The minimum number of edges in an F -saturatedsubgraph of G is denoted by sat(G,F ). Thus, sat(n, F ) is by definition equalto sat(Kn, F ).

In recent years, a new trend in extremal graph theory has been developed toextend the classical results, such as Ramsey’s and Turan’s theorems, to randomanalogues. The study reveals the behavior of extremal parameters for a typicalgraph. Recently, Korandi and Sudakov initiated the study of graph saturationfor the Erdos-Renyi random graphG(n, p). They proved for every fixed p ∈ (0, 1)and fixed integer r ≥ 3 that

sat(G(n, p),Kr

)=

(1 + o(1)

)n log 1

1−pn

with high probability. For the same values of p and r we show that with highprobability

sat(G(n, p),K1,r

)=

(r − 1)n

2− (

1 + o(1))(r − 1) log 1

1−pn,

where K1,r is the star graph on r + 1 vertices.This is a joint work with A. Mohammadian.

2010 Mathematics Subject Classifications : 05C35, 05C80Keywords: Random graph, Saturation, Star graph

School of Mathematics, Institute for Research in Fundamental Sci-

ences (IPM)




On Generalization of Group Rings and

Group Modules over G-sets

Mehmet Uc1

Abstract

Let G be a finite group, S a G–set, R a commutative ring with unity, M amodule over R. A G–set module denoted by MS is a set of all formal expressionof the form

∑s∈S mss where ms ∈M and ms = 0 for almost every s. We define

the sum in MS componentwise μ+η =∑

s∈S(ms+ns)s. The scalar product of∑s∈S mss by r ∈ R that is

∑s∈S(rms)s. Forρ =

∑g∈G rgg ∈ RG, the product

of∑

s∈S mss by ρ is

ρμ =∑s∈S

rgms(sg) =∑s′∈S

ms′s′ ∈MS, sg = s′ ∈ S.

MS is an RG–module with the structure defined above. Moreover, G–set mod-ules are generalization of both group rings and group modules.

In this paper, we prove some characterizations of G-set modules and decom-pose a given RG–module MS as a direct sum of RG–submodules. We will alsolook at some substructures of G–set modules. This paper also contains a theo-rem for the semisimplicity of a G–set module MS according to the propertiesof G, S, M and R.

2010 Mathematics Subject Classifications : 13A50, 16S34, 16D10, 16D70,20C05

Keywords: Group ring, Semisimple module, Group module, G-set

References

[1] I.G. Connell, On the group ring, Canadian J. Math. 15 (1963), 650–685.

[2] M.T. Kosan, T. Lee, Y. Zhou, On modules over group rings, Algebras and Rep-resentation Theory 17 (1) (2014), 87-102.

[3] D.S. Passmann, The Algebraic Structure of Group Rings, Dover Publications,Inc., New York, 2011.

1Mathematics Department, Burdur Mehmet Akif Ersoy University




Some Results On Prime And 2-Absorbing

Primary C-Ideals Of Multiplicative

Hyperrings

Neslihan Aytac1 , Gursel Yesilot2

Abstract

The multiplicative hyperrings were first introduced by R. Rota in 1982.Also primary hyperideal of a multiplicative hyperring have introduced by U.Dasgupta. 2- absorbing primary ideals and 2-absorbing ideals were studied byBadawi, Tekir and Yetkin in classic algebra. Here we mention about their hyperversions. First we write down the definitions of primary hyperideals, C-ideals,2-absorbing primary hyperideals of multiplicative hyperrings. R is a multiplica-tive hyperring and I is hyperideal of R similar to classic algebra. We mentionabout some properties about 2-absorbing prime and primary ideals and theirradicals. Also we proved theorems about relationship between 2-absorbing C-ideals of R and radicals of I. If I is a 2-absorbing primary C-ideal of R thenRad(I) is a 2-absorbing hyperideal of R. If Rad(I) is prime hyperideal, then I is2-absorbing primary hyperideal of R.

2010 Mathematics Subject Classifications : 20N20Keywords: multiplicative hyperring, primary hyperideal, radical, prime hyper-

ideal, C-ideal, 2- absorbing hyperideal, 2-absorbing primary hyperideal.

1Department of Mathematics, Yildiz Technical University,Turkey

2Department of Mathematics, Yildiz Technical University,Turkey




On the stabilizer of two dimensional vector

space of 27-dimensional module of type E6

over a field of characteristic two

Yousuf Alkhezi1 , Mashhour Bani Ata2

Abstract

The purpose of this paper is to examine general properties of the Tensorsand the Clifford Algebra: Special case Pinched Tensor Product. These proper-ties are compared to the analogue ordinary ones. The importance of this studycomes from the fact that the special case pinched tensor product has not muchbeen researched. The method is to replace the ordinary tensor product withthe Pinched tensor product. Also, in this paper we examine general propertiesof the pinched tensor product. These properties are compared to the analogueordinary ones. The study is extended to elaborate the reciprocity.

Mathematics subject classification: (2010) 15A66, 11E88, 20B25, 47A80.

Keywords: Clifford algebra, Geometric Algebra, Lie algebras, Tensor product,Pinched tensor product.

Acknowledgment

The author is grateful to Public Authority for Applied Education and Trainingfor supporting this research project No BE-17-22. Also, we are indebted to ProfessorM. ABUBAKAR HAGI for assistance in preparing the figures.

References

[1] Y. Benhadid, Y. Alkhezi. Clifford geometric algebra and compact wavelet support.International Mathematical Forum, Vol. 12, 2017, no. 11, 515-525.

[2] L. W. Christensen, D. A. Jorgensen, Tate (co)homology via pinched complexes.Trans. Amer. Math. Soc. 366, 2014, no. 2, 667-689.

[3] Y. Alkhezi. General properties of a morphism on the Pinched tensor product overassociative rings. Submitted.

[4] J. Rotman. An introduction to homological algebra. Second edition. Universitext.Springer, New York, 2009.

[5] A. Weibel. An introduction to homological algebra. Cambridge Studies in Ad-vanced Mathematics, 38. Cambridge University Press, Cambridge, 1994.

[6] A. Charlier, F. Daniele, A. Berard, and M. Charlier. Tensors and the Cliffordalgebra: Application to the physics of bosons and fermions, 1992.



[7] P. Lounesto. Clifford algebras and spinors. Vol. 286. Cambridge university press,2001.

1Department of Mathematics, College of Basic Education, Public

Authority for Applied Education and Training, Kuwait




Coefficient estimates for a class containing

quasi-convex functions of complex order

Oznur Ozkan Kılıc

Abstract

In this paper, we consider two subclasses of analytic functions of complexorder QCV (μ, b, A,B) and QST (η, b, A,B). The aim of paper is to determinecoefficient estimates of these classes.

2010 Mathematics Subject Classifications : 30C45Keywords: Analytic function, Subordination, Convex function, Starlike func-

tion, Quasi-convex function, Coefficient estimates, complex order

References

[1] O. Altıntas, On the coefficients of certain analytic functions, Math Japonica 33(1988), 653–659.

[2] O. Altıntas, H. Irmak, S. Owa, H.M. Srivastava, Coefficient bounds for somefamilies of starlike and convex functions of complex order, Appl Math Lett. 20(2007), 1218–1222.

[3] A.W. Goodman, Univalent Functions. Vol II. Somerset, NJ, USA: Mariner, 1983.

[4] Goodman AW. On close-to-convex functions of higher order, Ann Univ Sci Bu-dapest Eotvos Sect Math 1972; 15: 17-30.

[5] W. Janowski, Some extremal problems for certain families of analytic functions,Ann Polon Math. 28 (1973), 297-326.

Department of Technology and Knowledge Management, Baskent

University




A note on a subclass of analytic functions

Oznur Ozkan Kılıc

Abstract

The main objective of the present paper is to investigate coefficient estimatesfor a subclass of analytic functions. Also, certain consequences of them are given.

2010 Mathematics Subject Classifications : 30C45Keywords: Analytic function, Subordination, Convex function, Starlike func-

tion, Quasi-starlike function, Coefficient estimates.

References

[1] O. Altıntas, O. O. Kılıc, H.M. Srivastava, Neighborhoods of a certain family ofmultivalent functions with negative coefficients, Comp. Math. Appl. 47 (2004),1667–1672.

[2] O. Altıntas, H. Irmak, S. Owa, H.M. Srivastava, Coefficient bounds for somefamilies of starlike and convex functions of complex order, Appl Math Lett. 20(2007), 1218–1222.

[3] A.W. Goodman, Univalent Functions. Vol II. Somerset, NJ, USA: Mariner, 1983.

Department of Technology and Knowledge Management, Baskent

University




Minimax approximations and some

analytic inequalities with a parameter

Branko Malesevic1, Tatjana Lutovac1, Marija Rasajski1, Bojan Banjac2

Abstract

In this paper we consider minimax approximations and some families of ratio-nal mixed trigonometric functions ϕp(x) for x ∈ (0, π/2) and the real parameterp > 0. Symbolic-numerical methods that determine the value of the parameterp = p0 > 0 so that

minp∈R+

maxx∈(0,π/2)

|ϕp(x)| = maxx∈(0,π/2)

|ϕp0(x)|

are being developed. By selecting various families ϕp(x) and the parameter p > 0we obtain some well-known as well as some new analytic inequalities. Particu-larly, selecting p = p0 the properties of the corresponding analytic inequalitiesare considered.

2010 Mathematics Subject Classifications: 33B10, 26D05Keywords: minimax approximations, mixed polynomial trigonometric functions and

inequalities

1University of Belgrade, School of Electrical Engineering, Department of

Applied mathematics, Belgrade, Serbia


2University of Novi Sad, Faculty of Technical Sciences, Computer Graphics

Chair, Novi Sad, Serbia




2 POSTER PRESENTATIONS



Optical properties of Er3+ doped fluoride

single crystal

S. Khiari1,2 , M. Diaf2 , E. Boulma2 , C. Bensalem2

Abstract

We report on the spectroscopic investigation of Er3+ doped BaF2 single crys-tals. High-quality crystals have been gown by the Bridgman-Stockbarger pullingtechnique. The room temperature absorption, excitation, emission and fluores-cence decay spectra of the luminescent Er3+ ions inserted in BaF2 fluoride singlecrystals have been investigated. Using the Judd-Ofelt(JO) theory, the intensityparameters of Er3+ions have been calculated to be Ω2 = 0.949 × 10−20cm2,Ω4 = 0.975 × 10−20cm2 and Ω6 = 1.258 × 10−20cm2. These parameters werethen used to calculate the radiative transition probabilities (AJJ

′ ), branchingratios (βJJ

′ ) and radiative lifetimes (τrad) of the main laser emitting levels ofEr3+ions. The obtained spectroscopic properties are compared to those of Er3+

transitions in other fluoride and oxide hosts. The excitation spectrum in theUV–Visible spectral range is very close to the absorption spectrum indicatingthat all observed absorption levels can excite the Erbium green emission. Theemission spectrum is mainly dominated by the green emission alongside a weakred emission. For the main transitions, there is a good agreement between theemission spectrum and the spontaneous emission probabilities given by the JOanalysis. Using the Fuchtbauer–Ladenburg method, the emission cross-sectionof the three main visible emission were determined in addition to other impor-tant laser parameters such radiative quantum efficiency and optical gain.

Keywords: spectroscopic analysis, spectral parameters, Judd-Ofelt theory, laseremission.

1University of El-Tarf, El-Tarf 36000(Algeria)

2Laser Physics, Optical Spectroscopy and Optoelectronics Labora-

tory, Badji Mokhtar Annaba University, POB 12, 23000 Annaba (Alge-

ria)

E-mail : khiari [email protected]



Spectroscopic Study of Er3+ Doped CdF2

Single Crystal

F. Bendjedaa1 , M. Diaf2

Abstract

The objective of the work presented in this thesis focuses on the spectro-scopic properties of the MF2 (M = Cd, Sr) crystalline fluoride type dopedby rare earth ions. The cadmium fluoride (CdF2) crystals codoped by Erbiumfluoride (ErF3) and Ytterbium fluoride (Y bF3) were prepared using the Bridg-man’s method. The single crystals with the composition Cd0.7Sr0.3F2 of thepseudo-binary system CdF2 − SrF2 were obtained using the same techniqueafter purification of the starting materials. All the samples are of good opticalquality.

We have recorded absorption and emission spectra at room temperature.These spectra are exploited by the Judd-Ofelt theory (JO) in order to obtain thethree phenomenological parameters and the transition forces by the least squaremethod fitting. For the CdF2 matrix codoped with rare earth luminescent ionsEr+3 and Y b+3, the values of these parameters are: Ω2 = 1.057.10−20cm2,Ω4 = 0.524.10−20cm2, Ω6 = 1.108.10−20cm2 with a good root mean squaredeviation δ = 0.12.10−20cm2.

The calculation of the transition probabilities is in agreement with the in-tensities of the emission lines. We also explored the Stokes and anti-Stokesemissions of Er3+ ions codoping with the Y b3+ ions in this same matrix. Theseemissions showed an efficient energy transfer from Ytterbium to Erbium. Wemeasured for green and red emissions appreciable cross sections and metastablefluorescence lifetimes with high branching ratios showing the strong possibilityof obtaining laser emission along the wavelength of the emission line.

In the case of the matrix Cd0.7Sr0.3F2 : Er3+ (1%), Y b (4%) the obtainedvalues give a root mean square deviation δ = 0.066.10−20cm2 more refined thanthat of the CdF2 phase. The anti-Stokes emission spectrum obtained accordingto a multi-photon absorption mechanism is identical to that obtained by anothermechanism cited in the literature.

Keywords: Fluorure matrix, Judd-Ofelt, Absorption, Emission, Codoping, Anti-Stokes emission

1,2Laboratory of Laser Physics, Optical Spectroscopy and Optoelec-

tronics (LAPLASO), Badji Mokhtar Annaba University, POB 12, 23000,

Annaba, Algeria

E-mail : faiza [email protected]



On the coefficient bounds for general

subclasses of close-to-convex functions of

complex order

Serap Buluta

Abstract

In this work, we determine the coefficient bounds for functions in certain sub-classes of close-to-convex functions of complex order, which are introduced hereby means of a certain non-homogeneous Cauchy-Euler-type differential equationof order m. Relevant connections of some of the results obtained with those inearlier works are also provided.

2010 Mathematics Subject Classifications : 30C45, 30C50Keywords: Analytic functions, close-to-convex functions, Cauchy-Euler differ-

ential equations, coefficient bounds, subordination.

References

[1] O. Altıntas, H. Irmak, S. Owa and H.M. Srivastava, Coefficient bounds for somefamilies of starlike and convex functions of complex order, Appl. Math. Letters20 (2007), 1218–1222.

[2] O. Altıntas, O. Ozkan and H.M. Srivastava, Majorization by starlike functionsof complex order, Complex Variables Theory Appl. 46 (3) (2001), 207–218.

[3] S. Bulut, Coefficient bounds for certain subclasses of close-to-convex functions ofcomplex order, Filomat 31 (20) (2017), 6401-6408.

[4] G. Murugusundaramoorthy and H.M. Srivastava, Neighborhoods of certainclasses of analytic functions of complex order, J. Inequal. Pure Appl. Math. 5(2: Article 24) (2004), 1–8 (electronic).

[5] M.A. Nasr and M.K. Aouf, Radius of convexity for the class of starlike functionsof complex order, Bull. Fac. Sci. Assiut Univ. A 12 (1) (1983), 153–159.

[6] M.S. Robertson, On the theory of univalent functions, Ann. of Math. (2) 37 (2)(1936), 374–408.

[7] W. Rogosinski, On the coefficients of subordinate functions, Proc. London Math.Soc. (Ser. 2) 48 (1943), 48–82.

[8] H.M. Srivastava, O. Altıntas and S. Kırcı Serenbay, Coefficient bounds for certainsubclasses of starlike functions of complex order, Appl. Math. Lett. 24 (2011),1359–1363.

[9] H.M. Srivastava, Q.-H. Xu and G.-P. Wu, Coefficient estimates for certain sub-classes of spiral-like functions of complex order, Appl. Math. Lett. 23 (2010),763–768.



[10] W. Ul-Haq, A. Nazneen and N. Rehman, Coefficient estimates for certain sub-families of close-to-convex functions of complex order, Filomat 28 (6) (2014),1139–1142.

[11] W. Ul-Haq, A. Nazneen, M. Arif and N. Rehman, Coefficient bounds for certainsubclasses of close-to-convex functions of Janowski type, J. Comput. Anal. Appl.16 (1) (2014), 133–138.

[12] Q.-X. Xu, Q.-M. Cai and H.M. Srivastava, Sharp coefficient estimates for cer-tain subclasses of starlike functions of complex order, Appl. Math. Comput. 225(2013), 43–49.

[13] Q.-H. Xu, Y.-C. Gui and H.M. Srivastava, Coefficient estimates for certain sub-classes of analytic functions of complex order, Taiwanese J. Math. 15 (5) (2011),2377–2386.

aKocaeli University, Faculty of Aviation and Space Sciences, Arslan-

bey Campus, 41285 Kocaeli, Turkey.




Existence of Positive Solutions for a Class

of Second Order Impulsive Boundary Value

Problems on an infinite interval in Banach

Spaces

Ilkay Yaslan Karaca1 , Aycan Sinanoglu Arısoy2

Abstract

By using a fixed point theorem and constructing appropriate Banach space,we deal with the existence of positive solutions for a second-order impulsiveboundary value problem on the half-line.Some examples are presented to demon-strate the application of our main result.

2010 Mathematics Subject Classifications : 34B18, 34B37, 34B40Keywords: Impulsive Boundary Value Problems, Half-Line, Fixed Point Theo-

rem

References

[1] D. Guo, A class of second order impulsive integro-differential equations on un-bounded domain in a Banach space. Appl. Math. Comput. 125, 59-77 (2002).

[2] H. Chen, J. Sun, An application of variational method to second-order impulsivedifferential equations on the half line. Appl. Math. Comput., 217, 1863-1869 (2010)

[3] X. Zhao, W. Ge, Unbounded positive solutions for m-point time-scale boundaryvalue problem on infinite intervals, J. Appl. Math. Comput. 33 (2010) 103-123.

[4] X. Zhao, W. Ge, Existence of at least three positive solutions for multi-pointboundary value problem on infinite intervals with p-Laplacian operator, J. Appl.Math. Comput. 28 (2008) No. 1-2 391-403.

[5] D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones. AcademicPress, Boston (1988)

[6] D. Guo, Existence of two positive solutions for a class of second order impulsivesingular integro-differential equations on the half line, Boundary Value Problems,2015:76, 23pp.

[7] R.I. Avery, A generalization of the Leggett-Williams fixed point theorem, Math.Sci. Res. Hot- Line, 2 (1998) 9-14.

[8] R.P. Agarwal and D. O’Regan, Nonlinear boundary value problems on time scales.Nonlinear Anal. 44 (2001) 527-535.

[9] Y. Chen, B. Qin, Multiple positive solutions for first-order impulsive singularintegro-differential equations on the half line in a Banach space,Boundary ValueProblems, 69, (2013).



1Ege University, Izmir, Turkey

2Ege University, Izmir, Turkey



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