Browsing by Author "Duran, Ugur"
Now showing items 117 of 17

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. 16:4754, 2008) considered some relations in the context of quantum calculus associated with the qderivative operator Dq and divided difference. As applications of the postquantum calculus ... 
Construction of the type 2 polyFrobenius–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 polyBernoulli polynomials. Inspired by their work, we consider a new class of the Frobenius–Genocchi polynomials, which is called the type 2 ... 
Hermite based polybernoulli polynomials with a gparameter
Duran, Ugur; Acikgoz, Mehmet; Araci, Serkan (Jangjeon Mathematical Society, 2018)We introduce the Hermite based polyBernoulli 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 Hermitebased polyDaehee polynomials
Khan, Waseem Ahmad; Nisar, Kottakkaran Sooppy; Duran, Ugur; Acikgoz, Mehmet; Araci, Serkan (Natural Sciences Publishing USA, 20180301)In this paper, we introduce the generating function of Hermitebased polyDaehee numbers and polynomials. By making use of this generating function, we investigate some new and interesting identities for the Hermitebased ... 
A note on the (p,q)Hermite polynomials
Duran, Ugur; Acikgoz, Mehmet; Esi, Ayhan; Araci, Serkan (Natural Sciences Publishing USA, 20180101)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 rStirling numbers of the second kind based on the qnumbers via an exponential generating function. We investigate their some properties and derive several relations ... 
On applications of blending generating functions of qApostoltype polynomials
Duran, Ugur; Acikgoz, Mehmet; Araci, Serkan (BULGARIAN ACAD SCIENCE, 2019)Motivated by Kurt's blending generating functions of qApostol 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)FROBENIUSEULER POLYNOMIALS
Duran, Ugur; Acikgoz, Mehmet; Araci, Serkan (INST APPLIED MATHEMATICS, 2017)The main purpose of this paper is to introduce (p, q)FrobeniusEuler numbers and polynomials, and to investigate their some identities and properties including addition property, difference equation, derivative property, ... 
ON qGENOCCHI POLYNOMIALS WITH WEIGHTED alpha AND beta UNDER SYMMETRIC GROUP OF DEGREE n
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet (MILI PUBL, 201609)In this paper, we give some interesting identities for the modified qGenocchi polynomials with weight alpha and beta under symmetric group of degree n denoted by Sn arising from the fermionic padic qintegral on Z(p) 
On weighted qDaehee polynomials with their applications
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet (Elsevier B.V., 201903)In this paper, we first consider a generalization of Kim's padic qintegral on Z p including parameters α and β. By using this integral, we introduce the qDaehee polynomials and numbers with weight α,β. Then, we obtain ... 
Research on Some New Results Arising from Multiple qCalculus
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet (UNIV NIS, 2018)In this paper, we develop the theory of the multiple qanalogue of the Heine's binomial formula, chain rule and Leibniz's rule. We also derive many useful definitions and results involving multiple qantiderivative and ... 
Some (p, q)analogues of Apostol type numbers and polynomials
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet (UNIV TARTU PRESS, 201906)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 qGENOCCHI POLYNOMIALS UNDER S4
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet; Esi, Ayhan (UNIV PRISHTINES, 2015)In the paper, we derive some new symmetric identities of qGenocchi polynomials arising from the fermionic padic qintegral on Z(p). 
A study on a class of qEuler 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), 10771082], we study a class of qEuler polynomials earlier given by Kim et al. in [T. Kim, ... 
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 ApostolBernoulli, ApostolEuler and ApostolGenocchi polynomials of order alpha. By making ... 
(ρ,q)Volkenborn integration
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet (ACADEMIC PRESS INC ELSEVIER SCIENCE, 201702)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 ...