Special Issue "Recent developments in the areas of mathematics"

A special issue of Turkish Journal of Analysis and Number Theory

Deadline for manuscript submissions: (January 31, 2014)

Special Issue Editor(s)

Chief Guest Editor

Serkan Araci
University of Gaziantep
Email: mtsrkn@hotmail.com

Guest Editor

Mehmet Acikgoz
University of Gaziantep
Email: acikgoz@gantep.edu.tr

Guest Editor

Ilkay Arslan Güven
University of Gaziantep
Email: iarslan@gantep.edu.tr

Erdoğan Şen
Namik Kemal University
Email: erdogan.math@gmail.com

Special Issue Information

This issue contributes in the fied of almost all mathematics. An importance is placed on a vital and important developments in classical analysis, functional analysis, number theory, algebraic geometry, differential geometry, algebraic topology, mathematical analysis, mathematical physics, differential equations, quantum groups, and other parts of the natural sciences.


  • number theory
  • algebraic geometry
  • differential geometry
  • algebraic topology
  • mathematical analysis
  • mathematical physics
  • string theory
  • field theory
  • stochastic differential equations
  • quantum groups
  • and other parts of the natural sciences
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Published Papers

Abstract: This article takes the mathematical software Maple as the auxiliary tool to study the partial differential problem of two types of multivariable functions. We can obtain the infinite series forms of any order partial derivatives of these two types of functions by using differentiation term by term theorem, and hence greatly reduce the difficulty of calculating their higher order partial derivative values. On the other hand, we propose two examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying our answers by using Maple.
Abstract: We consider the hyper-geometric Daehee numbrers and polynomials and investigate some properties of those numbers and polynomials.
Abstract: The main objective of this paper is to introduce and investigate two new classes of generalized Apostol-Bernoulli polynomials Bn[m-1,α](x;c,α;λ) and Apostol-Euler polynomials εn[m-1,α](x;c,α;λ). In particular, we obtain addition formula for the new class of the generalized Apostol-Bernoulli polynomials. We also give some recurrence relations and Raabe relations for these polynomials.
Abstract: In this paper, using the difference operator and Orlicz functions, we introduce and examine some generalized difference sequence spaces of interval numbers. We prove completeness properties of these spaces. Further, we investigate some inclusion relations related to these spaces.
Abstract: In this study, we present generalized Fibonacci polynomials. We have used their Binet’s formula and generating function to derive the identities. The proofs of the main theorems are based on special functions, simple algebra and give several interesting properties involving them.
Abstract: The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second kind Stirling numbers and generalized Bernoulli polynomials. Moreover, we give the generating function and interpolation function of these modified q-Bernstein polynomials of two variables and also give the derivatives of these polynomials and their generating function.
Abstract: In this paper, we study a certain class of generalized Hurwitz-Lerch zeta functions. We derive several new and useful properties of these generalized Hurwitz-Lerch zeta functions such as (for example) their partial differential equations, new series and Mellin-Barnes type contour integral representations involving Fox’s H-function and a pair of summation formulas. More importantly, by considering their application in Number Theory, we construct a new continuous analogue of Lippert’s Hurwitz measure. Some statistical applications are also given.
Abstract: In this study, we give the relation of being general helix and slant helix of two curves by using the equation between them. Also we find some results and express the characterizations of these curves.
Abstract: In the present paper, we deal with multiple generalized Genocchi numbers and polynomials. Also, we introduce analytic interpolating function for the multiple generalized Genocchi numbers attached to χ at negative integers in complex plane and we de.ne the multiple Genocchi p-adic L-function. Finally, we derive the value of the partial derivative of our multiple p-adic l-function at s = 0.
Abstract: In this paper, our purpose is to show that Kannan Type and Chatterjea type contractive mappings have unique fixed point in b-metric spaces. Also, we see surprisingly a way that contrary to the known (usual) metric spaces, any contraction mapping is not need to be a weak conraction mapping in b-metric spaces.
Abstract: The -adic gamma functions associated with -extensions of Genocchi and Euler polynomials with weight were recently studied . By the same motivation, we aim in this paper to describe -analogue of -adic gamma functions with weight alpha and beta. Moreover, we give relationship between -adic -gamma functions with weight () and -extension of Genocchi numbers with weight alpha and beta and modified -Euler numbers with weight .
Abstract: The q-extension of Hardy-littlewood-type maximal operator in accordance with q Volkenborn integral in the p-adic integer ring was recently studied . A generalization of Jang's results was given by Araci and Acikgoz . By the same motivation of their papers, we aim to give the definition of the weighted q-Hardy-littlewood-type maximal operator by means of fermionic p-adic q-invariant distribution on Zp. Finally, we derive some interesting properties involving this-type maximal operator.
Abstract: In the present paper, we deal mainly with arithmetic properties of Legendre polynomials by using their orthogonality property. We show that Legendre polynomials are proportional with Bernoulli, Euler, Hermite and Bernstein polynomials.