THE 20 th INTERNATIONAL CONGRESS OF THE JANGJEON MATHEMATICAL SOCIETY

Transcription

1 THE 20 th INTERNATIONAL CONGRESS OF THE JANGJEON MATHEMATICAL SOCIETY August 21-23, 2008 Uludag University, Bursa-TURKIYE Supported by TÜBİTAK ( Uludag University ( Kültür Okulları( Emek Yağ ( Kafkas ( Edited by Dr. Ahmet TEKCAN ( August 21, 2008

2 2 The 20 th International Congress of The Jangjeon Mathematical Society COMMITTEES INTERNATIONAL SCIENTIFIC COMMITTEE DR. V. K. AATRE (INDIA) DR. R. P. AGARWAL (INDIA) DR. G. E. ANDREWS (USA) DR. K. AOMOTO (JAPAN) DR. B. C. BERNDT (USA) DR. H. BOR (TURKIYE) DR. J. BORWEIN (CANADA) DR. S. COOPER (NEW ZEALAND) DR. J. C. CORTET (FRANCE) DR. L. C. JANG (SOUTH KOREA) DR. T. KIM (SOUTH KOREA) DR. A. KRASSIMIN (BULGARIA) DR. H. K. PAK (SOUTH KOREA) DR. K. RAMACHANDRA (INDIA) DR. S. H. RIM (SOUTH KOREA) DR. I. SHIOKAWA (JAPAN) DR. A. SHTERN (RUSSIA) DR. Y. SIMSEK (TURKIYE) DR. K. N. SRINIVASARAO (INDIA) DR. H. M. SRIVASTAVA (CANADA) DR. X. WANG (CANADA) LOCAL ORGANIZING COMMITTEE DR. MUSTAFA YURTKURAN (RECTOR, ULUDAG UNIVERSITY) DR. GOKAY KAYNAK (DEAN, FACULTY OF ARTS & SCIENCE, ULUDAG UNIVERSITY) DR. VELI KURT (AKDENIZ UNIVERSITY) DR. YILMAZ SIMSEK (AKDENIZ UNIVERSITY) DR. ISMAIL NACI CANGUL (ULUDAG UNIVERSITY) DR. OSMAN BIZIM (ULUDAG UNIVERSITY) DR. METIN OZTURK (ULUDAG UNIVERSITY) DR. SIBEL YALCIN (ULUDAG UNIVERSITY) DR. A. SINAN CEVIK (BALIKESIR UNIVERSITY) DR. RECEP SAHIN (BALIKESIR UNIVERSITY) DR. AHMET TEKCAN (ULUDAG UNIVERSITY) DR. MUSA DEMIRCI (ULUDAG UNIVERSITY) DR. SEBAHATTIN IKIKARDES (BALIKESIR UNIVERSITY) HACER OZDEN (ULUDAG UNIVERSITY) ILKER INAM (ULUDAG UNIVERSITY) BETUL GEZER (ULUDAG UNIVERSITY) AYSUN YURTTAS (ULUDAG UNIVERSITY) Place: The conference will be held in Karinna Hotel ( at the famous ski resort Uludag.

3 The 20 th International Congress of The Jangjeon Mathematical Society 3 About The Jangjeon Mathematical Society (JMS) The Jangjeon Mathematical Society (JMS), born in historic Hapcheon, seeks to carry on Hapcheon s proud tradition of excellent scholarship coupled with unquestionable moral fidelity. Loyal to its Hapcheon heritage, JMS strives to maintain individual excellence, faithfulness to responsibility, and development of talents and abilities while adhering to core values of contributing to world peace and prosperity. JMS was founded in 1996 by Doctor Taekyun Kim to fulfill the aforementioned values through free discussion and cooperation amongst voluntarily participating scholars motivated by a common concern for the general welfare of mankind. This ideal of free and open discussion is mirrored by society s name, Jangjeon, which rendered in pure Korean, meaning Geul-Baat, the place of studies. With this significant symbolism in mind, Dr. Kim selected his birthplace, Jangjeon, as the title of this society. Since ancient times, Hapcheon has served as the training round of many scholars who carried on the teachings of the great Korean scholars, Namyoung Jo Sik, and were renowned for their utmost moral character and honor. The Hapcheon tradition of excellence may still be seen in its profound influence on many modern scholars. The geographical attributes of Hapcheon serve as fitting symbols of its metaphysical properties, The Hwang River, flowing serenely past suggests a steadfastness of virtue, unshaken by secular concerns, infusing energy into all living things. Nearby stands the towering Hwang-mae Mountain whose sheer slopes represent the unwavering fidelity of Hapcheon s scholars. There are many great scholars who are the members of JMS such as Dr. Seog-Hoon Rim (Managing Editor, Kyungpook University), Dr. Hari M. Srivastava (Chief, Victoria University), Dr. Alexander Shtern (Assistant Chief-in-Editors, Moscow State University), Dr. Krassimir Atanassov (Editor-in-Chief, Bulgarian Academy), Dr. Lee Chae Jang (Assistant-Managing Editor, Kunkook University), Dr. Hongkyung Pak (Adjustor, Daegu Haany University), Dr. Taekyun Kim (Founding Editor) etc. The 20th Congress of The Jangjeon Mathematical Society will be held in Uludag University, Bursa- TURKIYE. In conclusion, we are really appreciative of participants in the 20th Congress of The Jangjeon Mathematical Society and do hope that all participants, understanding the meaning of Jangjeon, enjoy this conference and work together for the development of world. We hope that all participants have free and active Jangjeon meaning Geul-Baat (place of studies) and meaningful discussions with other participants throughout the conference. Organizing Committee of the 20th Congress of The Jangjeon Mathematical Society.

4 4 The 20 th International Congress of The Jangjeon Mathematical Society About Bursa Bursa is a city in northwestern (called Marmara) of Turkiye and the seat of Bursa Province. The earliest known site at this location was Cius, which Philip V of Macedonia granted to the Bithynian king Prusias I in 202 BC, for his help against Pergamum and Heraclea Pontica (Karadeniz Ereğli). Prusias renamed the city after himself, as Prusa. It was later a major city, located on the westernmost end of the famous Silk Road, and was the capital of the Ottoman Empire following its capture from the shrinking Byzantine Empire in The capture of Edirne in 1365 brought that city to the fore as well, but Bursa remained an important administrative and commercial center even after it lost its status as the sole capital. Shortly after it was taken by the Ottomans they developed a school of theology at Bursa. This school attracted Muslim schoolers from throughout the Middle East and continued to function after the capital had been moved elsewhere. During the Ottoman rule, Bursa was the source of most royal silk products. Aside from the local production, it imported raw silk from Iran, and occasionally China, and was the factory for the kaftans, pillows, embroidery and other silk products for the royal palaces up through the 17th century. Another traditional occupation is knife making and, historically, horse carriage building. Nowadays one can still find hand-made knives as well as other products in rich variety produced by artisans, but instead of carriages, there are two big automobile industries FIAT and Renault. The city is frequently cited as Yeşil Bursa (meaning Green Bursa) in a reference to the beautiful parks and gardens located across its urban tissue, as well as to the vast forests in rich variety that extend in its surrounding region. The city is synonymous with the mountain Uludag (Olympus) which towers behind the city core and which is also a famous ski resort. The mausoleums of early Ottoman sultans are located in Bursa and the numerous edifices built throughout the Ottoman period constitute the city s main landmarks. The surrounding fertile plain, its thermal baths, several interesting museums, notably a rich museum of archaeology, and a rather orderly urban growth are further principal elements that complete Bursa s overall picture. At present, there is a population of approximately 2 Million and it is Turkiye s fourth largest city, as well as one of the most industrialized and culturally charged metropolitan centers in the country. Karagöz and Hacivat shadow play characters were historic personalities who lived and are buried in Bursa. Bursa is also home to some of the most famous Turkish dishes, especially candied chestnuts and İskender kebap. Its peaches are also well-renowned. Among its depending district centers, İznik (historic Nicaea), is especially notable for its long history and important edifices. Bursa is home to Uludag University which is one of the high-scale universities in Turkiye and in the international area. It has Academic staff and students at different levels, of them are undergraduates, 50 programs at 11 Faculties. It has one of the highest numbers, around 800, of foreign students amongst 102 Turkish universities because of its ongoing relationships at international arena.

5 The 20 th International Congress of The Jangjeon Mathematical Society 5 Foreword Dear Participants of The 20th International Congress of Jangjeon Mathematical Society, We warmly wellcome you all to the lovely city of Bursa and Uludağ University. As the members of The Mathematics Department at Uludağ University, we are proud of having the chance of organizing one of the Congresses of Jangjeon Mathematical Society. We would like to thank all members of the Society, Prof. Dr. Taekyun Kim and Prof. Dr. Seog-Hoon Rim in particular, for giving us the opportunity of bringing together such a nice group of people. The first words about Bursa which comes to ones mind are green, peaches, towels, candied chestnuts, Iskender (Döner) Kebap, history and industry. Being the first capital city of the Ottoman Empire, Bursa has its roots in the third century BC. But the recent findings proves that the real roots go back to 6000 BC. Having such a rich historical background, Bursa has a large number of archeological sites, together with ruins and monuments of many old cultures. Alongside this historical richness which makes it a touristical city, Bursa is one of the main industrial centers of Türkiye. Being at the one end of the famous silk road, there are thousands of Textile factories, three car factories - Fiat, Renault and Peugeot, and one can find a lot of other kinds of industrial production. Being placed on a large plateau, Bursa is also famous with agricultural products. Uludağ University hosting the congress is a middle aged University in Turkish standards. Being 33 years old, it has almost completed the infrastructure and human resources. It has concentrated on education and research in the last decade. As a result of these reforms, the number of publications has had increased five times. All the educational programs have been benchmarked with good universities in USA and Europe, which enabled the University to participate in many international projects and programmes. There are over 200 partner universities all over Europe with which Uludağ University is exchanging student and staff as well as academical knowledge. Mathematics Department is one of the oldest departments of the University which has been giving undergraduate and postgraduate education since Main research areas of the staff are Complex Analysis, Algebra, Discrete Group Theory, Number Theory, Elliptic Curves, p-adic Analysis, Differential Geometry, Projective Geometry, Mathematical Physics, Applications of Mathematics and Differential Equations. There is a total of 30 academic staff at the department which handles a high number of lectures in Mathematics, Physics, Chemistry, Biology Departments as well as all Engineering, Education and Agriculture Departments and 14 Vocational schools, and also carries research projects and other academical work. There is a high number of international partners of the Department and every year there are over 40 exchange students and a high number of visiting staff. Among these international partners, we are proud of having members of Jangjeon Mathematical Society in recent years which gave the chance to widen the research capacity of the Department members and the chance of organizing this memorable congress. We all hope that you enjoy the short period of time you will spend here and will try to create other chances to make your way to Uludağ University and Bursa again. Organizing Committee.

6 6 The 20 th International Congress of The Jangjeon Mathematical Society Gratitudes There are many people who spent a lot of time and effort to make this Congress possible. I would like to thank especially to the following young colleagues who had contributed to the success of this Congress in different ways: Dr. Ahmet TEKCAN (Editor) Res.Asst. İlker İNAM Res.Asst. Hacer ÖZDEN Res.Asst. Elif YAŞAR Res.Asst. Aysun YURTTAŞ Without their help, this Congress would be just a dream.

7 The 20 th International Congress of The Jangjeon Mathematical Society 7 Contents 1 On Sums of Squares Chandrashekar Adiga 14 2 Some Abstract Convex Functions and Hermit-Hadamard Type Inequalities Gabil Adilov and Serap Kemali 15 3 Neighborhoods of Multivalent Analytic Functions Osman Altıntaş 16 4 Determination of Limit Cycles by Homotopy Perturbation Method for Nonlinear Oscillators Bahar Arslan and Ahmet Yıldırım 17 5 Geometric Approximations to Minimality of Monoids Firat Ateş and Ahmet Sinan Çevik 18 6 On Some Properties of the Spaces A p(x) w (R n ) Ismail Aydın and A.Turan Gürkanlı 19 7 New Complete Monotonicity Properties of the Gamma Function Necdet Batır 20 8 On Values of Jacobi Forms and Shifted Elliptic Dedekind Sums Abdelmejid Bayad 21 9 A Modular Transformation for a Generalized Theta Function with Multiple Parameters S.Bhargava, M.S.Mahadeva Naika and M.C.Maheshkumar On Meromorphic Harmonic Starlike Functions with Missing Coefficients Hakan Bostanci and Metin Öztürk The Effect of Optically Thick Limit and Buoyancy Forces on the Stability of MHD Ekman Layer Mabrouk Bragdi and Mahdi Fadel Mosa A Note on the Operator-Valued Poisson Kernel Serap Bulut A Generalization of Zakrzewski Morphisms Mădălina Roxana Buneci Some Closed Type Formulas for Bernoulli and Related Numbers Mehmet Cenkci On Neighborhood Number and its Related Parameters in Graphs B.Chaluvaraju The Thermal Properties of the Deformation Potential Materials in Circularly Oscillating Fields J.Y.Choi, J.Y.Sug, S.H.Lee, S.C.Park and Sa-Gong Geon 29

8 8 The 20 th International Congress of The Jangjeon Mathematical Society 17 Permutation Polynomials on Finite Fields Mihai Cipu On the Eigenvalues of a Schrödinger Operator with Matrix Potential Didem Coṣkan and Sedef Karakılıç Weak Solutions in Asymmetric Elasticity Ion Al.Crăciun Tauberian Theorems for Abel Limitability Method Ibrahim Çanak and Ümit Totur On (1 u 2 )-cyclic Codes over F 2 k + uf 2 k + u 2 F 2 k Yasemin Çengellenmis (L, M)-intuitionistic Fuzzy Filters Vildan Çetkin, Banu Pazar, Halis Aygün Determination of Unknown Boundary Condition in a Quasi-linear Parabolic Equation Ali Demir and Ebru Özbilge A Quasilinear Elliptic System with Integral Boundary Conditions Mohammed Derhab On the q-trigonometric, q-hyperbolic Functions Ayhan Dil and Veli Kurt A Fixed Point Theorem Hülya Duru On The Vague DeMorgan Complemented Partially Ordered Sets and Lattices Zeynep Eken Application of He s Semi-Inverse Method to the Nonlinear Wave Equations Meryem Erdal and Ahmet Yıldırım A System of ODEs for Nonlinear Programming Problems with Smooth Penalty Function Fırat Evirgen and Necati Özdemir B(X, X )-Valued Kernels and B(X )-Modules Păstorel Gaşpar and Dimitru Gaşpar Singular Curves and Singular Elliptic Divisibility Sequences over Finite Fields Betül Gezer, Osman Bizim and Ahmet Tekcan τ c -Topology on Hypergroup Algebras Ali Ghaffari Application of Statistical Shape Analysis to the Classification of Renal Tumours Appearing in Early Childhood Stefan Markus Giebel 46

9 The 20 th International Congress of The Jangjeon Mathematical Society 9 34 Kac-Moody-Virasoro Algebras as Symmetries of 2+1-dimensional Nonlinear Partial Differential Equations Faruk Güngör Trigonometric Approximation of Functions in Weighted L p Spaces Ali Güven Approximation by Means of Fourier Trigonometric Series in Weighted Orlicz Spaces Ali Güven and Daniyal M.Israfilov Finite Derivation Type for Graph Products of Monoids Eylem Güzel On the Rational Operator Pencils in Banach Space Elman Hasanov Note On Generalized M*-Groups Sebahattin Ikikardes and Recep Şahin Periodic Solutions for Singular Perturbation Problem of 2 Dimensional Dynamical System Under Matching Conditions Mohammed Jahanshahi On The Weighted Composition Operators Khadijeh Jahedi and Sedigheh Jahedi Morita Equivalence and Outer Conjugacy of Dynamical Systems Maria Joita Entanglement Dynamics in Stochastic Atom-Field Interactions Hünkar Kayhan Elementary Abelian Coverings of Regular Hypermaps of Types {5, 5, 5} and {5, 2, 10} of Genus 2 Mustafa Kazaz Some Subordination Results for Certain Analytic Functions of Complex Order Involving Carlson-Shaffer Operator Öznur Özkan Kılıç Arrays with the Window Property and their Generalization Sang-Mok Kim p-adic q-integration on Z p Taekyun Kim On a Inverse and Direct Problems of Scattering Theory for a Class of Sturm-Liouville Operator with Discountinous Coefficient Nida Palamut Koşar and Khanlar R.Mamedov 61

10 10 The 20 th International Congress of The Jangjeon Mathematical Society 49 Surfaces with Negative Gauss Curvature; Classification According to the Singularities of Attached Monogenous Functions Lidia Elena Kozma Integral and Difference Inequalities in Several Independent Variables and their Discrete Analogues Emine Mısırlı Kurpınar and Özlem Moğol Rothe s Method for Semilinear Parabolic Integrodifferential Equation with Integral Condition A.Guezane-Lakoud and Abderrezak Chaoui The Magnetic Field Dependence of the Quantum Transition Properties of Si in the Linearly Polarized Oscillating Field S.H.Lee, J.Y.Sug, G.H.Rue, Sa-Gong Geon and J.Y.Choi Gnan Mean and its Dual in Several Arguents Veerabhadraiah Lokesha Non-linear Multi-objective Transportation Problem: A Fuzzy Goal Programming Approach Hamid Reza Maleki and Sara Khodaparasti Recursive Relations on the Coefficients of Some p-adic Differential Equations Hamza Menken and Abdulkadir Aşan On N(k)-Mixed Quasi Einstein Manifolds H.G.Nagaraja Some New Explicit Values for Ramanujan Class Invariants M.S.Mahadeva Naika The Necessarily Efficient Point Method for Interval MOLP Problems Hassan Mishmast Nehi and Marzieh Alineghad Application of Variational Iteration Method for Solving Some Partial Differential Equations Volkan Oban and Ahmet Yıldırım The Limit q-bernstein Operator Sofiya Ostrovska Verification of the Unknown Diffusion Coefficient by Semigroup Method Ebru Özbilge and Ali Demir Fractional Optimal Control Problem in Cylindrical Coordinates Necati Özdemir, Derya Karadeniz and Beyza B.Iskender Remarks on Interpolation Functions of q-bernoulli Numbers Hacer Özden, Ismail Naci Cangül and Yilmaz Simsek 76

11 The 20 th International Congress of The Jangjeon Mathematical Society Non-local Gas Dynamics Equation and Invariant Solutions Teoman Özer A Note on Multiplers of L p (G, A) Serap Öztop On the Numerical Solutions of Bitsadze Samarskii Type Elliptic Equation with Nonlocal Boundary and Mixed Conditions Elif Öztürk and Allaberen Ashyralyev Notes on Multiplicative Calculus Ali Özyapıcı and Emine Mısırlı Kurpınar Interval-valued L-fuzzy Topological Groups Banu Pazar, Vildan Çetkin and Halis Aygün Binomial Thue Equations and their Applications Akos Pinter, Michael Bennett, Kalman Gyory, Lajos Hajdu and Istvan Pink A Distributional Approach to Classical Electromagnetism I: The Mathematical Tools Burak Polat A Distributional Approach to Classical Electromagnetism II: The Physical Evidences Burak Polat Numerical Study of non-darcy Forced Convective Heat Transfer in a Power Law Fluid over a Stretching Sheet K.V.Prasad and V.Rajappa Note on Genocchi Numbers and Polynomials Seog-Hoon Rim, Kyoung Ho Park, Yong Do Lim and Eun Jung Moon Generalized Sobolev-Shubin Spaces Ayşe Sandıkçı and A.Turan Gürkanlı On Tripotency and Idempotency of Some Linear Combinations of Two Commuting Quadripotent Matrices Murat Sarduvan and Halim Özdemir On Double Lacunary Statistical σ-convergence of Fuzzy Numbers Ekrem Savaş An Excursion into the World of Elliptic Hypergeometric Series Michael J.Schlosser Some Properties of Vague Rings Sevda Sezer Beta-Semigroup and Riesz Potentials Sinem Sezer and Ilham A.Aliev 92

12 12 The 20 th International Congress of The Jangjeon Mathematical Society 80 Principle of Local Conservation of Energy-Momentum Garret Sobczyk and Tolga Yarman Concerning Fundamental Mathematical and Physical Defects in the General Theory of Relativity Garret Sobczyk, Stephen J.Crothers and Tolga Yarman The Diophantine Equation x m = y n Gökhan Soydan, Musa Demirci and Ismail Naci Cangül Fuzzy Triangular Inequality Gültekin Soylu Bounds for Classical Orthogonal Polynomials and Related Special Functions H.M.Srivastava Some Glimpses of Hindu (or Vedic) Mathematics and Srinivasa Ramanujan ( ) Rekha Srivastava On p-adic q-dedekind Sums Yılmaz Şimşek On Quadratic Ideals and Indefinite Quadratic Forms Ahmet Tekcan, Osman Bizim and Betül Gezer Improved Direct and Inverse Theorems of Approximation Theory in the Morrey- Smirnov Classes Defined on the Complex Plane N.Pınar Tozman and Daniyal M.Israfilov On q Laplace Type Integral Operators and their Applications Faruk Uçar and Durmuş Albayrak q-laplace Transforms Burcu Vulaş and Gülsen Kürem Relative Defect and Multiple Common Roots of Two Meromorphic Functions Harina P.Waghamore The Quantum Mechanical Mechanism Behind the end Results of the GTR: Matter is Built on the Lorentz Invariant Framework Energy x Mass x Length 2 h 2 Tolga Yarman Some Applications of He s Variational Approaches Ahmet Yıldırım An Efficient Method for Solving Singular Two-Point Initial Value Problems Ahmet Yıldırım and Deniz Ağırseven Holditch Theorem for the Closed Space Curves in Lorentzian 3-space Handan Yıldırım, Salim Yüce and Nuri Kuruoğlu 108

13 The 20 th International Congress of The Jangjeon Mathematical Society On the Numerical Solutions of Hyperbolic Equations with Nonlocal Boundary and Neumann Conditions Özgür Yıldırım and and Allaberen Ashyralyev The Estimation of Mean Modulus of Smoothness in L p w Yunus Emre Yildirir and Daniyal Israfilov Differential Transform Method (DTM) for Solving Sine-Gordon Type Equations Eda Yülüklü and Turgut Öziş Hardy Littlewood and Polya Inequalities and their Applications to Various Integral Transforms Osman Yürekli On Sum Degree Energy of a Graph R.K.Zaferani, C.Adiga and H.B.Walıkar A Goal Programming Method for Finding Common Weights in DEA Majid Zohrehbandian, Ahmad Makui and Alireza Alinezhad 114

14 14 The 20 th International Congress of The Jangjeon Mathematical Society 1 On Sums of Squares Chandrashekar Adiga Historically one of the problems receiving a good deal of attention is the representing integers as sums of squares. In this talk, we first briefly review some of the advances in this area and then we describe how Ramanujan s continued fractions are useful in deriving Jacobi s two-square and two-triangular theorems. Finally, we present a general relationbetween sums of squares and sums of triangular numbers. [1] Adiga C. and Vasuki K.R. On sums of triangular numbers. The Mathematics Student 70(2001), [2] Adiga C. Cooper S. and Han J.H. A general relation between sums of squares and sums of triangular numbers. Int. Jour. Number Theory 1(2)(2005), [3] Barrucand P. Cooper S. and Hirschhorn M. Relations between squares and triangles. Discrete.Math. 248(1-3)(2002), [4] Berndt B.C. Ramanujan s Notebooks. Part III, Springer-Verlag,New York, Address: Department of Studies in Mathematics, University of Mysore, Manasagangotri, Myore INDIA adiga c@yahoo.com

15 The 20 th International Congress of The Jangjeon Mathematical Society 15 2 Some Abstract Convex Functions and Hermit-Hadamard Type Inequalities Gabil Adilov and Serap Kemali Studying Hermite-Hadamard type inequalities for some function classifications have been very important in recent years. These inequalities, which are known in convex functions, are also found in different function classifications ([4-5], [7]). One of these functions classifications is abstract convex functions. The problem of finding Hermite-Hadamard type inequalities for increasing positively homogeneous (IPH) functions, increasing radiant (InR) functions, increasing co-radiant (ICR) functions and increasing convex-alongrays (ICAR) functions, which are significant classifications of abstract convex functions, is investigated by different authors and the concrete results are found ([1, 2, 3, 6, 8]). In this article, the problem of calculating Hermit-Hadamard type inequalities is considered totally, older results are summarized, new results of some classification are achieved and the results of some other classification are generalized. By considering a concrete area in R 2 ++, all the results defined for that specific area. [1] Adilov G.R. and Kemali S. Hermite-Hadamard type inequalities for increasing positively homogeneous functions. Journal of Inequalities and Applications, Volume 2007, Article ID 21430, 10pp, dor /2007/ [2] Adilov G.R. Increasing co-radiant functions and Hermite-Hadamard type inequalities. Mathematical Inequalities and Applications (Submitted). [3] Dragomir S.S., Dutta J. and Rubinov A.M. Hermite-Hadamard type inequalities for increasing convex along rays functions. Analysis (Munich) 24(2), [4] Dragomir S.S. and Pearce C.E.E. Quasi-convex functions and Hadamard s inequality. Bull. Australian Math. Soc. 57(1998), [5] Pearce C.E.M. and Rubinov A.M. P-functions, quasiconvex functions and Hadamard-type inequalities. Journal of Mathematical Analysis and Applications 240(1999), [6] Rubinov A.M. Abstract convexity and global optimization. Kluwer Academic Publishers, Dordrecht, [7] Rubinov A.M. and Dutta J. Hadamard type inequality for quasiconvex functions in higher dimensions. (Preprint) RGMIA Res. Rep. Coll., 4 (1) (2001), Article 9. [ONLINE: rgmia.vu.edu.au/v4n1.htm1] [8] Sharikov E.V. Hermite-Hadamard type inequalities for increasing radiant functions. Journal of Inequalities in Pure and Applied Mathematics 4(2)(2003), Article 47. Address: Mersin University, Faculty of Arts and Science, Department of Mathematics, Mersin-TURKIYE Akdeniz University, Faculty of Arts and Science, Department of Mathematics, Antalya-TURKIYE s: gabil@mersin.edu.tr, skemali@akdeniz.edu.tr

16 16 The 20 th International Congress of The Jangjeon Mathematical Society 3 Neighborhoods of Multivalent Analytic Functions Osman Altıntaş Let T (n, p) denote the class of functions f(z) which are analytic and multivalent in the unit disk U = {z : z C and z < 1}. We define the (n, ε) neighborhood of a function f (q+δ) (z) when f T (n, p). We also let Tn,p q (λ, α, δ) denote the subclass of T (n, p) consisting of functions f (z) which satisfy the following inequality Re zf (1+q+δ) (z) + λz 2 f (2+q+δ) (z) λzf (1+q+δ) (z) + (1 λ)f (q+δ) (z) > α, where 0 λ 1, 0 δ < 1, 0 α < p q δ, p > q, p N, q N 0 = N {0}. Finally K n (p, q, δ, α, λ, µ) denote the subclass of the general class T (n, p) consisting of functions f T (n, p) which satisfy the following non-homogenous Cauchy-Euler differential equation: z 2 d2+q+δ w dz 2+q+δ + 2 (1 + µ) z d1+q+δ w dz 1+q+δ + µ (1 + µ) dq+δ w dz q+δ = (p q δ + µ) (p q δ + µ + 1) dq+δ g dz q+δ, where w = f T (n, p), g Tn,p q (λ, α, δ) and µ > q p + δ. In the present investigation, several results concerning the (n, ε) neighborhoods, coefficient bounds, distortion inequalities for functions f T (n, p) in both classes Tn,p q (λ, α, δ) and K n (p, q, δ, α, λ, µ) are given. [1] Altıntaş O. On a subclass of certain starlike functions with negative coefficients. Math. Japonica 36 (1991), [2] Altıntaş O., Irmak H. and Srivastava H.M. Fractional calculus and certain starlike functions with negative coefficients. Comput. Math. Appl. 30(2)(1995), [3] Altıntaş O., Özkan Ö. and Srivastava H.M. Neighborhoods of a certain family of multivalent functions with negative coefficients. Comput. Math. Appl. 47(2004), [4] Altıntaş O. Neighborhoods of certain p-valently analytic functions with negative coefficients. Appl. Math. and Computation 187(2007), Address: Baskent University, Department of Mathematics Education, Baglıca, TR 06530, Ankara-TURKIYE oaltintas@baskent.edu.tr

17 The 20 th International Congress of The Jangjeon Mathematical Society 17 4 Determination of Limit Cycles by Homotopy Perturbation Method for Nonlinear Oscillators Bahar Arslan and Ahmet Yıldırım In this paper, Homotopy perturbation method is applied to certain nonlinear oscillators with strong nonlinearity. The method is of deceptively simplicity and the insightful solutions obtained are of high accuracy even for the first-order approximations. [1] He JH. Non-Perturbative Methods for Strongly Nonlinear Problems. Dissertation.de- Verlag im Internet GmbH, 2006 [2] He JH. Some asymptotic methods for strongly nonlinear equations. International Journal of modern Physics B 20(10)(2006), [3] He JH.Limit cycle and bifurcation of nonlinear problems. Chaos Solitons & Fractals 26(3)(2005), [4] He JH. Determination of limit cycles for strongly nonlinear oscillators. Physical Review Letters 90(17)(2003), Art. No [5] Özis T. and Yıldırım A. A note on He s homotopy perturbation method for van der Pol oscillator with very strong nonlinearity. Chaos Solitons & Fractals 34(3)(), [6] Özis T. and Yıldırım A. Determination of limit cycles by a modified straightforward expansion for nonlinear oscillators. Chaos Solitons & Fractals 32(2007), Address: Ege University, Faculty of Science, Department of Mathematics, Bornova 35100, Izmir-TURKIYE s: baharernam@hotmail.com, ahmet.yildirim@ege.edu.tr

18 18 The 20 th International Congress of The Jangjeon Mathematical Society 5 Geometric Approximations to Minimality of Monoids Firat Ateş and Ahmet Sinan Çevik It was mainly considered a geometric configuration, namely pictures, of monoid presentations. In fact, by using pictures, we showed that a specific monoid presentation (that is, the presentation of the semidirect product of finite cyclic monoids) is minimal while it is inefficient. Let A and K be arbitrary two monoids. For any connecting monoid homomorphism θ : A End(K), let M = K θ A be the corresponding monoid semi-direct product. In [2], Cevik clarified necessary and sufficient conditions for the standard presentation M of M to be p-cockcroft for any prime p or 0. Moreover, as an application of this above result, it has been showed the efficiency for the presentation M of the semidirect product of any two finite cyclic monoids (in a joint work [1]). As a main tool of this talk, it will be given sufficient conditions for M to be minimal but not efficient. To do that the same method in [2] will be used. The fundamental material of arbitrary semigroups can be found in the famous book [3]. We also note that while the geometric thecniques of semigroups (and also of monoids) have been studied in [4, 5], the homological methods and applications have been specified in [3]. Finally an application of the geometric part has been given on the semidirect product of monoids in [7]. [1] Ateş F. and Çevik A.S. Minimal but inefficient presentations for semidirect product of finite cyclic monoids. Groups St. Andrews 2005, Vol 1, L.M.S. Lecture Note Series, 339(2006), [2] Çevik A.S. Minimal but inefficient presentations of the semi-direct products of some monoids. Semigroup Forum 66(2003), [3] Howie J.M. Fundamentals of Semigroup Theory. Oxford University press, [4] Pride S.J. Geometric methods in combinatorial semigroup theory. Semigroups, Formal Languages and Groups, (J.Fountain editor), Kluwer Academic Publishers, (1995). [5] Pride S.J. Low-dimensional homotopy theory for monoids. Int. J. Algebra and Comput. 5(6)(1995), [6] Squier C.C. Word problems and a homological finiteness condition for monoids. Journal of Pure and Appl. Algebra 49(1987), [7] Wang J. Finite derivation type for semi-direct products of monoids. Theoretical Computer Science, 191(1-2)(1998), Address: Balikesir University, Faculty of Science and Arts, Department of Mathematics, Cagis Campus, 10145, Balikesir-TURKIYE s: firat@balikesir.edu.tr, scevik@balikesir.edu.tr URLL: scevik/

19 The 20 th International Congress of The Jangjeon Mathematical Society 19 6 On Some Properties of the Spaces A p(x) w (R n ) Ismail Aydın and A.Turan Gürkanlı In this work we define A p(x) w (R n ) to be the vector space of all complex-valued functions in L 1 w (R n ) whose Fourier transforms f belong to the generalized Lebesgue space L p(x) (R n ), where p (x) is a measurable function from R n into [1, ). We endow it with the sum norm f p w = f 1,w + f and study some p important properties of this space. Furthermore we show that A p(x) w investigate the ideals of the space A p(x) w and compact embeddings between the spaces A p(x) w (R n ) is a S w (R n ) space [1]. Later we (R n ). At the end of this work we discuss inclusions, embedding (R n ) and the multipliers of the spaces Aw p(x) (R n ). [1] Cigler J. Normed ideals in L 1 (G). Indag Math. 31(1969), Address: Sinop University, Faculty of Arts and Sciences, Department of Mathematics, 57000, Sinop-TURKIYE Ondokuz Mayıs University, Faculty of Arts and Sciences, Department of Mathematics, Kurupelit, Samsun-TURKIYE s: ismaila@omu.edu.tr, gurkanli@omu.edu.tr

20 20 The 20 th International Congress of The Jangjeon Mathematical Society 7 New Complete Monotonicity Properties of the Gamma Function Necdet Batır As it is well known the classical gamma function is defined by the integral Γ(z) = 0 u z 1 e u du, for Rez > 0. In this talk, we prove some new complete monotonicity theorems for this important function. [1] Alzer H. Gamma function inequalities. Numer. Algor. DOI / , [2] Alzer H. and Batir N. Monotonicty properties of the gamma function. Appl. Math. Lett. 20(2007), [3] Alzer H. Inequalities fo the gamma function. Proc. Amer. Math. Soc. 128(1999), [4] Alzer H. and Grinshpan A.Z. Inequalities for the gamma and q-gamma functions. J. Approx. Theory 144(2007), [5] Alzer H. and Berg C. Some Classes of completeley monotonic functions II. The Ramanujan Journal 11(2)(2006), [6] Alzer H. On Ramanujan s Double inequality for the gamma function. Bull. London Math. Soc. 35(2003), [7] Alzer H. On some inequalities for the gamma and psi functions. Math. Comp. 66(217)(1997), [8] Anderson G.D., Barnard R.W., Richards K.C., Vamanamurthy M.K. and Vuorinen M. Inequalities for zero-balanced hypergeometric functions. Trans Amer. Math. Soc. 347(1995), [9] Andrews G., Askey R., and Toy R. Special functions, Encyclopedia of Mathematics and its Applications. V.71, Cambridge U. Pres, [10] Batir N. Sharp inequalities for factorial n. Proyecciones 27(1)(2008), [11] Batir N. On some properties of the gamma function. Expo. Math. 26(2008), [12] Batir N. Some new inequalities for gamma and polygamma functions. JIPAM. J. Inequal. Pure Appl. 6(4)(2005), Article 103, 9 pp. [13] Burnside W. A rapidly convergent series for logn!. Messenger Math. 46(1917), Address: Yüzüncü Yil University, Faculty of Sciences and Arts, Department of Mathematics, 65080, Van-TURKIYE necdet batir@hotmail.com

21 The 20 th International Congress of The Jangjeon Mathematical Society 21 8 On Values of Jacobi Forms and Shifted Elliptic Dedekind Sums Abdelmejid Bayad It s well known that the Jacobi forms in one variable are a cross between elliptic functions and modular forms in one variable. They have several applications in differents areas in mathematics, especially in number theory and arithmetical geometry [6]. In this talk, we are interesting by the study of values of some Jacobi forms in two variables. Precisely, we introduce shifted elliptic Dedekind sums in terms of special values of Jacobi forms in two variables and we state and prove their reciprocity Laws. In our study, we show how to use our techniques to obtain a closed new reciprocity law for the so-called Shifted-elliptic Dedekind-Sczech Sums. [1] Atiyah M.F. The Logarithm of the Dedekind-Function. Math. Ann 278(1987), [2] Barge J. and Ghys E. Cocycles d Euler et de Maslov. Math. Ann. 294(2)(1992), [3] Maria Immaculada Galvez Carrillo. Modular invariants for manifolds with Boundary. Thesis (2001), [4] Hirzebruch F. The signature theorem: reminiscences and recreation. Prospects in Mathematics. Ann. of Math.Studies 70, 3-31, Princeton University Press, Princeton, [5] Hirzebruch F., Berger T. and Jung R. Manifolds and Modular forms. Aspects of Math.E. 20, Vieweg (1992). [6] Hirzebruch F. and Zagier D. The Atiyah-Singer Theorem and Elementary Number Theory. Math. Lecture Series 3, Publish or Perish Inc, [7] Kirby R. and Melvin P. Dedekind sums, µ-invariants and the signature cocycle. Math. Annalen 299(1994), [8] Sczech R. Dedekindsummen mit elliptischen Funktionen. Invent.math 76(1984), [9] Weselmann U. EisensteinKohomologie und Dedekindsummen fur GL 2 uber imaginarquadratischen Zahlenkorpern. J. reine. angew. Math. 389(1988), Address: Departement de mathematiques, Universit e d Evry Val d Essone Bd. F. Mitterrand, EVRY CEDEX abayad@maths.univ-evry.fr

22 22 The 20 th International Congress of The Jangjeon Mathematical Society 9 A Modular Transformation for a Generalized Theta Function with Multiple Parameters S.Bhargava, M.S.Mahadeva Naika and M.C.Maheshkumar In this talk, We obtain a modular transformation for the theta function q a(m2 +mn)+cn 2 +λm+µn+ν ζ Am+Bn z Cm+Dn. (9.1) We are thus able to unify and extend several modular transformations in literature. We also establish the relations between the above identity and Jacobian Theta-function when a b. The objective here is to obtain a modular transformation for (9.1). It is possible to first treat the above equation(9.1) with λ = µ = ν = 0, A = B = 1 = C, D = 1 and then effect suitable transformations on ζ and z to obtain our main result. But we have preferred to present our main result and all the related lemmas directly and in detail in order to bring out the motivation and lucidity of the inter play between the various parameters all through, than would be the case in the abbreviated alternative approach. [1] Adiga C., Berndt B.C., Bhargava S. and Watson G.N. Chapter 16 of Ramanujan s Second Notebook, Theta functions and q-series. Mem. Am. Math. Soc. 53, no. 315(1985), American Mathematical Society, Providence, [2] Adiga C., Mahadeva Naika M.S. and Han J.H. General Modular Transformations for Theta Functions. Indian J. Math. 49(2)(2007), [3] Baker H.F. An Introduction to the Theory of Multiply Periodic Functions. Cambridge University Press, (1907). [4] Bellmen R. A Brief Introduction to the theta functions. Holt, Rinehart and Winston, (1961). [5] Bhargava S. Unification of the Cubic Analogues of Jacobian Theta Functions. J. Math. Anal. Appl. 193(1995), [6] Bhargava S. and Anitha N. A Triple Product Identity for the three parameter Cubic Theta Function. Indian Journal of Pure and Applied Math. 36(9)(2005), [7] Bhargava S. and Fathima S.N. Unification of Modular Transformations for Cubic Theta Functions. New Zealand J. Mathematics 33(2004), [8] Borwein J.M. and Borwein P.B. A Cubic Counterpart of Jacobi s Identity and the AGM. Trans. Amer. Math. Soc. 323(1991), [9] CooperS. Cubic Theta Functions. J. Computational and Applied Math. 160(2003), [10] Hecke E. Mathematische Werks. Göttingen: Vordenhoeck und Ruprecht, Address: Department of studies in Mathematics, University of Mysore, Manasagangotri, Mysore , INDIA Department of Mathematics, Bangalore University, Central College Campus, Bangalore , INDIA Department of Mathematics, Bangalore University, Central College Campus, Bangalore , INDIA s: srinivasamurthyb@yahoo.com, msmnaika@rediffmail.com, softmahe@rediffmail.com

23 The 20 th International Congress of The Jangjeon Mathematical Society On Meromorphic Harmonic Starlike Functions with Missing Coefficients Hakan Bostanci and Metin Öztürk In this paper, we introduce a new class of meromorphic harmonic starlike functions with missing coefficients in the punctured unit disk U = {z : 0 < z < 1}. We obtain coefficient inequalities, distortion theorem and closure theorem. In addition, we investigated some properties of this class. [1] Cluine J. and Sheil-Small T. Harmonic Univalent Functions. Ann. Acad. Sci. Fenn. Ser. Al Math. 9 (1984), [2] Hengartner W. and Schober G. Univalent Harmonic Functions. Trans. Amer. Math. Soc. 299 (1987), [3] Jahangari J.M. Coefficient bounds and univalence criteria for harmonic functions with negative coefficients. Ann. Univ. Mariae Currie-Sklodowska, Sec. A, 52(1998), [4] Jahangari J.M. Harmonic Meromorphic Starlike Functions. Bull. Korean Math. Soc. 37(2)(2000), [5] Auf M.K. and Hossen H.M. New criteria for meromorphic p-valent starlike funcitons. Tsukuba J. Math. 17(2)(1993), [6] Darwish H.E. Meromorphic p-valent starlike functions with negative coefficients. Indian J. Pure Apll. Math. 33(7)(2002), [7] Uraleggaddi B.A. and Somanatha C. New criteria for meromorphic starlike univalent functions. Bull. Austral. Math. Soc. 43(1991), [8] Joshi S.B. and Sangle N.D. Meromorphic Starlike functions with negative and missing coefficients. Far East J. Math. Sci. (FMJS) 26(2)(2007), [9] Jahangari J.M. and Silverman H. Meromorphic Univalent Harmonic Functions with Negative Coefficients. Bull. Korean Math. Soc. 36(1999), [10] Murugusundaramoorthy G. Starlikeness of multivalent meromorphic harmonic functions. Bull. Korean Math. Soc. 40(4)(2003), [11] Murugusundaramoorthy, G. Harmonic meromorphic convex functions with missing coefficients, J. Indones. Math. Soc. (MIHMI), 10(1)(2004), Address: Uludag University, Faculty of Science, Department of Mathematics, Görükle 16059, Bursa-TURKIYE s: hbostanci@uludag.edu.tr, ometin@uludag.edu.tr

24 24 The 20 th International Congress of The Jangjeon Mathematical Society 11 The Effect of Optically Thick Limit and Buoyancy Forces on the Stability of MHD Ekman Layer Mabrouk Bragdi and Mahdi Fadel Mosa Let us consider a Cartesian co-ordinate system of rotating uniformly with angular velocity Ω about the z-axis, the basic equations of motion for such a configuration in a non-dimensional form, as well established (cf. [3]): v t u u t Ev S η = 3D N(u 1) + 2 u η 2 v + E(u 1) S η = 3D Nv + 2 v η ( ( θ t S θ η = 3D 1 2 θ P r η Ec Q 2 Bo η + Ec u η ) 2 + ( v η F r ) ) Grθ 2 + NEc The boundary conditions on velocities and temperature can be written in the form: ((u 1) 2 + v 2 ). u = 3Dv = 3D0 at η = 3D0; u 1, v 0 as η. θ = 3D1 at η = 3D0 for suction; θ = 3D T T 0 at η = 3D0 for blowing; θ = 3D T T 0 as η. A radiative optically thick limit case has been introduce into the energy equation of MHD Ekman layer. A steady solution for the velocity and temperature distribution is obtained by using a finite difference method that implements the 3-stage lobatto IIIa formula, the resulting solution have shown that the radiation has a remarkable effect on the temerature distribution. Also the stability of this model is investigated. The differential equations governing such a stability problem are introduced. A computer program for computing the eigenvalues of the system for the measured of the stability has been organized using Matlab V.6, and the neutral stability curves have been achievement at difference cases of parameters. The result of the mathematical analysis show that the optically thick limit and buoyancy forces produced a new addition case for stability. [1] Helliwell J.B. On the stability of thermally radiative = magnetofluiddynamic channel flow. J. Eng. Math. 11(1977), [2] Helliwell J.B. and Mosa M.F. Radiative heat transfer= in horizontal magnetohydrodynamic channel flow with buoyancy effects and an axial temperature gradient. Int. J. Heat Mass Transfer 22(1979), [3] Mosa M.F. Radiative heat transfer in MHD Ekman layer on a porous plate. Dirasat: The University of Jordan, 7(2)(1985), 167. [4] Mosa M.F. and Manaa S.A. Effects of radiative heat=transfer in the MHD Ekman layer on a porous plate. Mu tah Journal for Research and Studies, Natural and Applied Sciences Series, 7(1992), 286. Address: University Center of Larbi Ben M hidi, Department of Mathematics, route de Constantine, DZ Oum El Bouaghi-ALGERIA bravdi@yahoo.com

25 The 20 th International Congress of The Jangjeon Mathematical Society A Note on the Operator-Valued Poisson Kernel Serap Bulut In this talk, we give a different proof of the integral formula 1 2π 2π where K r,t (T ) is the operator-valued Poisson kernel. 0 K r,t (T )dt = I, [1] Chalendar I. The operator-valued Poisson kernel and its applications. Ir. Math. Soc. Bull. 51(2003), [2] Taylor A.E. A Note on the Poisson Kernel. Amer. Math. Monthly 57(1950), Address: Kocaeli University, Faculty of Arts and Science, Department of Mathematics, Kocaeli-TURKIYE serap.bulut@kou.edu.tr

26 26 The 20 th International Congress of The Jangjeon Mathematical Society 13 A Generalization of Zakrzewski Morphisms Mădălina Roxana Buneci We briefly recall various notions of groupoid morphisms and their applications. Then we introduce a new notion of groupoid morphisms (in algebraic setting as well as in topological setting), starting from the characterization obtained in [1] for the Zakrzewski morphisms [8]. The classes of (algebraic, respectively, topological) groupoids with these new introduced morphisms form categories. We also prove that the isomorphisms of the resulted categories can be identified with the groupoid isomorphisms in the usual sense. We analyze the relation between the proposed notion of groupoid morphisms and other notions such as correspondences [7], bibundles [3] and we show that these new morphisms are generalizations of the morphisms in the sense of [8, 2]. [1] Buneci M. Groupoid categories. Perspectives in Operator Algebras and Mathematical Physics 27-40, Theta [2] Buneci M. and Stachura P. Morphisms of locally compact groupoids endowed with Haar systems. arxiv: math.oa/ [3] Landsman N.P. Operator algebras and Poisson manifolds associated to groupoids. Comm. Math. Phys. 222(2001), [4] Muhly P., Reanult J. and Williams D. Equivalence and isomorphism for groupoid C*-algebras. J. Operator Theory 17(1987), [5] Muhly P. Coordinates in operator algebra. Book in preparation. [6] Renault J. A groupoid approach to C -algebras. Lecture Notes in Math. Springer-Verlag, 793, [7] Macho-Stadler M. and O Uchi M. Correspondences and groupoids. Proceedings of the IX Fall Workshop on Geometry and Physics, Publicaciones de la RSME 3(2000), [8] Zakrzewski S. Quantum and Classical pseudogroups I. Comm. Math. Phys. 134(1990), Address: Department of Mathematics, University Constantin Brncui, Bld. Republicii, Nr. 1, Trgu Jiu- ROMANIA ada@utgjiu.ro

27 The 20 th International Congress of The Jangjeon Mathematical Society Some Closed Type Formulas for Bernoulli and Related Numbers Mehmet Cenkci The object of this talk is to give further applications of the theorem relating to potential polynomial and exponential Bell polynomial stated by Howard [Discrete Math. 39 (1982) ]. This theorem provides a methodical approach to a number of formulas and identities involving Stirling numbers. In particular, we derive several closed form formulas for higher order Bernoulli, Eulerian, Genocchi, tangent, Apostol-Bernoulli, Apostol-Euler, Bernoulli numbers of the second kind and the numbers A (z) n. [1] Apostol T.M. On the Lerch zeta function. Pacific J. Math. 1(1951), [2] Carlitz L. Eulerian numbers and polynomials. Math. Mag. 33(1959), [3] Carlitz L. A note on Bernoulli and Euler polynomials of the second kind. Scripta Math. 25(1961), [4] Cenkci M. and Howard F.T. Notes on degenerate numbers. Discrete Math. 307(2007), [5] Comtet L. Advanced Combinatorics. Riedel, Dordrech, Boston, [6] Gould H.W. Combinatorial Identites. Morgantown, [7] Howard F.T. A sequence of numbers related to the exponential function. Duke Math. J. 34(1967), [8] Howard F.T. Numbers generated by the reciprocal of e x x 1. Math. Comput. 31(1977), [9] Howard F.T. A special class of Bell polynomials. Math. Comput. 35(1980), [10] Howard F.T. A theorem relating potential and Bell polynomials. Discrete Math. 39(1982), [11] Jordan C. Calculus of Finite Differences. Chelsea, New York, [12] Luo Q.-M. and Srivastava H.M. Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials. J. Math. Anal. Appl. 308(2005), [13] Luo Q.-M. and Srivastava H.M. Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials. Comput. Math. Appl. 51(2006), [14] Nörlund N. Vorlesungen über Differenzenrechnung. Chelsea, New York, [15] Srivastava H.M. and Todorov P.G. An explicit formula for the generalized Bernoulli polynomials. J. Math. Anal. Appl. 130(1988), [16] Todorov P.G. Une formule simple explicite des nombres Bernoulli généralisés. C. R. Acad. Sci. Paris Sér. I Math. 301(1985), Address: Akdeniz University, Department of Mathematics, Antalya-TURKIYE cenkci@akdeniz.edu.tr

28 28 The 20 th International Congress of The Jangjeon Mathematical Society 15 On Neighborhood Number and its Related Parameters in Graphs B.Chaluvaraju Given a simple graph G = (V, E), a subset S of V is called a neighborhood set provided G is the union of the subgraphs induced by the closed neighborhoods of the vertices in S. The neighborhood number η(g) of G is the minimum cardinality of a neighborhood set of G. In this paper, we initiate a study on neighborhood set and its related parameters and also its graph theoretical relationships are explored. [1] Chaluvaraju B. k-neighborhood, k-connected neighborhood and k-co-connected neighborhood number of a graph. J.of Analysis and Computation 3(1)(2007), [2] Harary F. Graph theory. Addison-Wesley, Reading Mass [3] Haynes T.W., Hedetniemi S.T and Slater P.J. Fundamentals of domination in graphs. Marcel Dekker, Inc., New York, [4] Hedetniemi S.M., Hedetniemi S.T, Laskar R.C, Markus L. and Slater P.J. Disjoint dominating sets in graphs. Proce. of Int. Conf. of Disct. Maths., IISc, Bangalore, (2006), [5] Jayaram S.R. The nomatic number of a graph. Nat. Acad. Sci. Lett. 19(1996), [6] Kulli V.R. and Sigarkanti S.C. Further results on the neighbourhood number of a graph. Indian J. Pure and Appl. Math. 23(8)(1992), [7] Kulli V.R. and Soner N.D. The independent neighbourhood number of a graph. Nat. Acad. Sci. Letts. 19(1996), [8] Sampathkumar E. and Neeralagi P.S. The neighbourhood number of a graph. Indian J. Pure and Appl. Math. 16(2)(1985), [9] Soner N.D., Chaluvaraju B. and Janakiram B. The maximal neighborhood number of a graph. Far East J. Appl. Math. 5(3)(2001), [10] Soner N.D., Chaluvaraju B. and Janakiram B. Maximal edge neighborhood number in graphs. Indian Math. Soc. (IMS) 46(2-3)(2004), Address: Department of Mathematics, Central College Campus, Bangalore University, Bangalore INDIA bchaluvaraju@yahoo.co.in