Browsing by Author "Duran, Ugur"
Now showing items 1-19 of 19
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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 ... -
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 ... -
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 ... -
Multifarious implicit summation formulae of Hermite-based poly-Daehee polynomials
Khan, Waseem Ahmad; Nisar, Kottakkaran Sooppy; Duran, Ugur; Acikgoz, Mehmet; Araci, Serkan (Natural Sciences Publishing USA, 2018-03-01)In this paper, we introduce the generating function of Hermite-based poly-Daehee numbers and polynomials. By making use of this generating function, we investigate some new and interesting identities for the Hermite-based ... -
A note on the (p,q)-Hermite polynomials
Duran, Ugur; Acikgoz, Mehmet; Esi, Ayhan; Araci, Serkan (Natural Sciences Publishing USA, 2018-01-01)In this paper, we introduce a new generalization of the Hermite polynomials via (p,q)-exponential generating function and investigate several properties and relations for mentioned polynomials including derivative property, ... -
On (p,q)-Bernoulli, (p,q)-Euler and (p,q)-genocchi polynomials
Duran, Ugur; Acikgoz, Mehmet; Araci, Serkan (American Scientific Publishers, 2016)In the present paper, we introduce a new kind of Bernoulli, Euler and Genocchi polynomials based on the (p,q)-calculus and investigate their some properties involving addition theorems, difference equations, derivative ... -
ON (q, r, w)-STIRLING NUMBERS OF THE SECOND KIND
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet (UNIV PRISHTINES, 2018)In this paper, we introduce a new generalization of the r-Stirling numbers of the second kind based on the q-numbers via an exponential generating function. We investigate their some properties and derive several relations ... -
On applications of blending generating functions of q-Apostol-type polynomials
Duran, Ugur; Acikgoz, Mehmet; Araci, Serkan (BULGARIAN ACAD SCIENCE, 2019)Motivated by Kurt's blending generating functions of q-Apostol polynomials [16], we investigate some new identities and relations. We also aim to derive several new connections between these polynomials and generalized ... -
ON HIGHER ORDER (p, q)-FROBENIUS-EULER POLYNOMIALS
Duran, Ugur; Acikgoz, Mehmet; Araci, Serkan (INST APPLIED MATHEMATICS, 2017)The main purpose of this paper is to introduce (p, q)-Frobenius-Euler numbers and polynomials, and to investigate their some identities and properties including addition property, difference equation, derivative property, ... -
ON q-GENOCCHI POLYNOMIALS WITH WEIGHTED alpha AND beta UNDER SYMMETRIC GROUP OF DEGREE n
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet (MILI PUBL, 2016-09)In this paper, we give some interesting identities for the modified q-Genocchi polynomials with weight alpha and beta under symmetric group of degree n denoted by S-n arising from the fermionic p-adic q-integral on Z(p) -
On weighted q-Daehee polynomials with their applications
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet (Elsevier B.V., 2019-03)In this paper, we first consider a generalization of Kim's p-adic q-integral on Z p including parameters α and β. By using this integral, we introduce the q-Daehee polynomials and numbers with weight α,β. Then, we obtain ... -
Research on Some New Results Arising from Multiple q-Calculus
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet (UNIV NIS, 2018)In this paper, we develop the theory of the multiple q-analogue of the Heine's binomial formula, chain rule and Leibniz's rule. We also derive many useful definitions and results involving multiple q-antiderivative and ... -
Some (p, q)-analogues of Apostol type numbers and polynomials
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet (UNIV TARTU PRESS, 2019-06)We consider a new class of generating functions of the generalizations of Bernoulli and Euler polynomials in terms of (p, q)-integers. By making use of these generating functions, we derive (p, q)-generalizations of several ... -
SOME NEW SYMMETRIC IDENTITIES INVOLVING q-GENOCCHI POLYNOMIALS UNDER S-4
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet; Esi, Ayhan (UNIV PRISHTINES, 2015)In the paper, we derive some new symmetric identities of q-Genocchi polynomials arising from the fermionic p-adic q-integral on Z(p). -
A study on a class of q-Euler polynomials under the symmetric group of degree n
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet (INT SCIENTIFIC RESEARCH PUBLICATIONS, 2016)Motivated by the paper of Kim et al. [T. Kim, D. S. Kim, H. I. Kwon, J. J. Seo, D. V. Dolgy, J. Nonlinear Sci. Appl., 9 (2016), 1077-1082], we study a class of q-Euler polynomials earlier given by Kim et al. in [T. Kim, ... -
A STUDY ON SOME NEW RESULTS ARISING FROM (p, q)-CALCULUS
Duran, Ugur; Acikgoz, Mehmet; Araci, Serkan (INST APPLIED MATHEMATICS, 2020)This paper includes some new investigations and results for post quantum calculus, denoted by (p, q)-calculus. A chain rule for (p, q)-derivative is given. Also, a new (p, q)-analogue of the exponential function is introduced ... -
Unified (P, q)-analog of apostol type polynomials of order α
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet (UNIV NIS, 2018)In this work, we introduce a class of a new generating function for (p, q)-analog of Apostol type polynomials of order a including Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order alpha. By making ... -
(ρ,q)-Volkenborn integration
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2017-02)In the paper, we introduce an analogue of Haar distribution based on (rho, q)-numbers, as follows: mu(rho,q) (a + p(N)Z(p)) = rho(pN)/[p(N)](rho,q) (q/rho)(a) By means of this distribution, we derive (rho, q)-analogue ...