arXiv subjects
Publications and source records attributed to Mehmet Acikgoz.
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 \c{hi} at negative integers in complex plane and we define 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.
In the present paper, our objective is to treat a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order Dedekind-type sums with weight in connection with modified q-Genocchi polynomials with weight alpha by using p-adic invariant q-integral on Zp.
In the present paper, we deal with Fourier-transformation of Frobenius-Euler polynomials. We shall give its applications by using infinite series. Our applications possess interesting properties which we state in this paper.
In the present paper, our goal is to introduce a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order dedekind-type sums with weight alpha related to Extended q-Euler polynomials by using p-adic q-integral in the p-adic integer ring.
In this paper, we focus on the q-Genocchi numbers and polynomials. We shall introduce new identities of the q-Genocchi numbers and polynomials by using the fermionic p-adic integral on Zp which are very important in the study of Frobenius-Genocchi numbers and polynomials. Also, we give Cauchy-integral formula for the q-Genocchi polynomials and moreover by using measure theory on p-adic integral we derive the distribution formula q-Genocchi polynomials. Finally, we present a new definition of q-Zeta-type function by using Mellin transformation which is the interpolation function of the q-Genocchi polynomials at negative integers.
In the present paper, we effect Dirichlet's type of twisted Eulerian polynomials by using p-adic fermionic q-integral on the p-adic integer ring. Also, we introduce some new interesting identities for them. As a result of them, by using contour integral on the generating function of Dirichlet's type of twisted Eulerian polynomials and so we define twisted Eulerian-L-function which interpolates of Dirichlet's type of Eulerian polynomials at negative integers which we state in this paper.
In the present paper, we introduce Eulerian polynomials attached to by using p-adic q-integral on Zp . Also, we give new interesting identities via the generating functions of Dirichlet's type of Eulerian polynomials. After, by applying Mellin transformation to this generating function of Dirichlet' type of Eulerian polynomials, we derive L-function for Eulerian polynomials which interpolates of Dirichlet's type of Eulerian polynomials at negative integers.
We give some new identities for (h; q)-Genocchi numbers and polynomials by means of the fermionic p-adic q-integral on Zp and the weighted q-Bernstein polynomials.
In the present paper, we investigate special generalized q-Euler numbers and polynomials. Some earlier results of T. Kim in terms of q-Euler polynomials with weight alpha can be deduced. For presentation of our formulas we apply the method of generating function and p-adic q-integral representation on Zp. We summarize our results as follows. In section 2, by using combinatorial techniques we present two formulas for q-Euler numbers with weight alpha. In section 3, we derive distribution formula (Multiplication Theorem) for Dirichlet type of q-Euler numbers and polynomials with weight . Moreover we define partial Dirichlet type zeta function and Dirichlet q-L-function, and obtain some interesting combinatorial identities for interpolating our new definitions. In addition, we derive behavior of the Dirichlet type of q-Euler L-function with weight alpha, Lq (s; x j) at s = 0. Furthermore by using second kind stirling numbers, we obtain an explicit formula for Dirichlet type q-Euler numbers with weight alpha. Moreover a novel formula for q-Euler-Zeta function with weight in terms of nested series of E;q (n j) is derived . In section 4, by introducing p-adic Dirichlet type of q-Euler measure with weight, and we obtain some combinatorial relations, which interpolate our previous results. In section 5, which is the main section of our paper. As an application, we introduce a novel concept of dynamics of the zeros of analytically continued q-Euler polynomials with weight alpha.
The present paper deals with Bernstein polynomials and Frobenius-Euler numbers and polynomials. We apply the method of generating function and fermionic p-adic integral representation on Zp, which are exploited to derive further classes of Bernstein polynomials and Frobenius-Euler numbers and polynomials. To be more precise we summarize our results as follows, we obtain some combinatorial relations between Frobenius-Euler numbers and polynomials. Furthermore, we derive an integral representation of Bernstein polynomials of degree n on Zp . Also we deduce a fermionic p-adic integral representation of product Bernstein polynomials of different degrees n1, n2,...on Zp and show that it can be written with Frobenius-Euler numbers which yields a deeper insight into the effectiveness of this type of generalizations. Our applications possess a number of interesting properties which we state in this paper.
The fundamental aim of this paper is to define weighted q-Hardy-littlewood-type maximal operator by means of fermionic p-adic q-invariant distribution on Zp . Also, we derive some interesting properties concerning this type maximal operator.
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.
In this paper, we shall investigate and analyse a new study on the best simultaneous approximation in the context of linear 2-normed spaces inspired by Elumalai and his coworkers in Elumalai. The basis of this investigation is to extend and refinement the definition of the classical aproximation, best approximation and some related concepts to linear 2-normed spaces.
In this work, we consider the generating function of Kim's q-Euler polynomials and introduce new generalization of q-Genocchi polynomials and numbers of higher order. Also, we give surprising identities for studying in Analytic Numbers Theory and especially in Mathematical Physics. Moreover, by applying q-Mellin transformation to generating function of q-Genocchi polynomials of higher order and so we define q-Hurwitz-Zeta type function which interpolates of this polynomials at negative integers.
In the present paper, we analyse analytic continuation of weighted q-Genocchi numbers and polynomials. A novel formula for weighted q-Genocchi- Zeta function ζG,q (s | α) in terms of nested series of ζG,q (n | α) is derived. Moreover, we introduce a novel concept of dynamics of the zeros of analytically continued weighted q-Genocchi polynomials.
In this paper, we deal with q-Euler numbers and q-Bernoulli numbers. We derive some interesting relations for q-Euler numbers and polynomials by using their generating function and derivative operator. Also, we show between the q-Euler numbers and q-Bernoulli numbers via the p-adic q-integral in the p-adic integer ring.
In this paper, the authors deal with the $q$-Genocchi numbers and polynomials with weight zero. They discover some interesting relations via the $p$-adic $q$-integral on $\mathbb{Z}_{p}$ and familiar basis Bernstein polynomials. Finally, the authors show that the $p$-adic $\log$ gamma functions are associated with the $q$-Genocchi numbers and polynomials with weight zero.
The essential aim of this paper is to define weighted q-Hardy-littlewood-type maximal operator by means of p-adic q-invariant distribution on Zp. Moreover, we give some interesting properties concerning this type maximal operator.