Browsing by Author "Acikgoz, Mehmet"
Now showing items 1-20 of 52
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An analogue of Eulerian polynomials related to L-type function
Araci, Serkan; Acikgoz, Mehmet; Corcino, Roberto B.; Ozel, Cenap (MAEJO UNIV, 2015-05)We introduce Dirichlet's type of twisted Eulerian polynomials by using p-adic fermionic q-invairant integral in the p-adic integer ring and obtain some new interesting identities. Using a complex contour integral representation ... -
Analogues of Newton-Girard power-sum formulas for entire and meromorphic functions with applications to the Riemann zeta function
Araci, Serkan; Bagdasaryan, Armen; Acikgoz, Mehmet; Srivastava, H. M. (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2015-02)The Newton power-sum formulas relate to sums of powers of roots of a polynomial with the coefficients of the polynomial. In this paper we obtain formulas that relate to sums of reciprocal powers of zeros and poles of entire ... -
Applications of fourier series and zeta functions to Genocchi polynomials
Araci, Serkan; Acikgoz, Mehmet (Natural Sciences Publishing, 2018-09-01)In this paper, we firstly consider the properties of Genocchi polynomials, Fourier series and Zeta functions. In the special cases, we see that the Fourier series yield Zeta functions. From here, we show that zeta functions ... -
Asymptotic properties of a new Sturm-Liouville problem with retarded argument
Araci, Serkan; Acikgoz, Mehmet; Sen, Erdogan (WILEY-BLACKWELL, 2014-11-30)In this work, we study the asymptotic properties of a new Sturm-Liouville problem with retarded argument. Contrary to previous works, differential equation includes eigenparameter as a quadratic function. In the considered ... -
Bell-Based Bernoulli Polynomials with Applications
Duran, Ugur; Araci, Serkan; Acikgoz, Mehmet (MDPI, MAR 2021)In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations and properties including some summation formulas related to the Bell polynomials and Stirling numbers of the ... -
A certain (p, q)-derivative operator and associated divided differences
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet; Srivastava, H. M. (SPRINGEROPEN, 2016)Recently, Sofonea (Gen. Math. 16:47-54, 2008) considered some relations in the context of quantum calculus associated with the q-derivative operator D-q and divided difference. As applications of the post-quantum calculus ... -
Certain fractional calculus formulas involving extended generalized Mathieu series
Araci, Serkan; Singh, Gurmej; Agarwal, Praveen; Acikgoz, Mehmet (SPRINGEROPEN, 2018-04-23)We establish fractional integral and derivative formulas by using fractional calculus operators involving the extended generalized Mathieu series. Next, we develop their composition formulas by applying the integral ... -
A Class of Generating Functions for a New Generalization of Eulerian Polynomials with their Interpolation Functions
Araci, Serkan; Sen, Erdogan; Acikgoz, Mehmet (UNIV NIS, 2016)Motivated by a number of recent investigations, we define and investigate the various properties of a new family of the Eulerian polynomials. We derive useful results involving these Eulerian polynomials including (for ... -
Computation of Nevanlinna characteristic functions derived from generating functions of some special numbers
Araci, Serkan; Acikgoz, Mehmet (SPRINGER INTERNATIONAL PUBLISHING AG, 2018-06)In the present paper, firstly we find a number of poles of generating functions of Bernoulli numbers and associated Euler numbers, denoted by n(a, B) and n(a, E), respectively. Secondly, we derive the mean value of a ... -
Construction of a New Class of Generating Functions of Binary Products of Some Special Numbers and Polynomials
Boughaba, Souhila; Boussayoud, Ali; Araci, Serkan; Kerada, Mohamed; Acikgoz, Mehmet (UNIV NIS, 2021)In this paper, we derive some new symmetric properties of k-Fibonacci numbers by making use of symmetrizing operator. We also give some new generating functions for the products of some special numbers such as k-Fibonacci ... -
Construction of a new class of symmetric function of binary products of (p, q)-numbers with 2-orthogonal Chebyshev polynomials
Saba, Nabiha; Boussayoud, Ali; Araci, Serkan; Kerada, Mohamed; Acikgoz, Mehmet (Birkhauser, March 2021)In this paper, we give some new generating functions of the products of (p, q)-Fibonacci numbers, (p, q) -Lucas numbers, (p, q)-Pell numbers, (p, q) -Pell Lucas numbers, (p, q)-Jacobsthal numbers, and (p, q)-Jacobsthal ... -
Construction of Fourier expansion of Apostol Frobenius-Euler polynomials and its applications
Araci, Serkan; Acikgoz, Mehmet (SPRINGEROPEN, 2018-02-22)In the present paper, we find the Fourier expansion of the Apostol Frobenius-Euler polynomials. By using a Fourier expansion of the Apostol Frobenius-Euler polynomials, we derive some new and interesting results. -
Construction of the type 2 poly-Frobenius–Genocchi polynomials with their certain applications
Duran, Ugur; Acikgoz, Mehmet; Araci, Serkan (Springer, 1 December)Kim and Kim (Russ. J. Math. Phys. 26(1):40–49, 2019) have studied the type 2 poly-Bernoulli polynomials. Inspired by their work, we consider a new class of the Frobenius–Genocchi polynomials, which is called the type 2 ... -
Existence and uniqueness of positive and nondecreasing solutions for a class of fractional boundary value problems involving the p-Laplacian operator
Araci, Serkan; Sen, Erdogan; Acikgoz, Mehmet; Srivastava, H. M. (SPRINGER INTERNATIONAL PUBLISHING AG, 2015-02-11)In this article, we investigate the existence of a solution arising from the following fractional q-difference boundary value problem by using the p-Laplacian operator: D-q(gamma)(phi(p)(D(q)(delta)y(t))) + f(t,y(t)) = 0 ... -
FULLY DEGENERATE HERMITE POLY-BERNOULLI NUMBERS AND POLYNOMIALS
Khan, Waseem Ahmad; Nisar, Kottakkaran Sooppy; Araci, Serkan; Acikgoz, Mehmet (MILI PUBL, 2018-04)In the paper, we first introduce the fully degenerate Hermite poly-Bernoulli polynomials and investigate their properties. Next we derive the implicit summation formulae and general symmetry identities by making use of ... -
A General Class of the Three-Variable Unified Apostol-Type q-Polynomials and Multiple Power q-Sums
Srivastava, Hari M.; Khan, Subuhi; Araci, Serkan; Acikgoz, Mehmet; Riyasat, Mumtaz (Springer International Publishing, 2019)The main purpose of this article is to introduce a general class of the three-variable unified Apostol-type q-polynomials and to investigate their properties and characteristics. In particular, the generating function, ... -
Generalized Szasz-Kantorovich Type Operators
Kajla, Arun; Araci, Serkan; Goyal, Meenu; Acikgoz, Mehmet (RGN PUBL, 2019)In this note, we present Kantorovich modification of the operators introduced by V. Mihesan [Creative Math. Inf. 17 (2008), 466 - 472]. First, we derive some indispensable auxiliary results in the second section. We present ... -
Generating functions of binary products of k-Fibonacci and orthogonal polynomials
Araci, Serkan; Kerada, Mohamed; Acikgoz, Mehmet; Boughaba, Souhila; Boussayoud, Ali (SPRINGER-VERLAG ITALIA SRL, 2019-07)In this paper, we introduce a new operator in order to derive some new symmetric properties of k-Fibonacci and k-Pell numbers and Tchebychev polynomials of first and second kind. By making use of the new operator defined ... -
Hermite based poly-bernoulli polynomials with a g-parameter
Duran, Ugur; Acikgoz, Mehmet; Araci, Serkan (Jangjeon Mathematical Society, 2018)We introduce the Hermite based poly-Bernoulli polynomials with a q parameter and give some of their basic properties including not only addition property, but also derivative properties and integral representations. We ... -
Identities on Some Special Poynomials Derived from the Concepts of n-Normed Structures, Accretive Operators and Contraction Mappings
Araci, Serkan; Kir, Mehmet; Dutta, Hemen; Acikgoz, Mehmet (SPRINGER INTERNATIONAL PUBLISHING A, 2018-06)In this paper, we study the notions of accretive operators, contraction mappings, non-expansive mappings using the idea of n (>l)-normed structures for some relevant results. Further, we define (lambda, q)-transform by ...
