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- Yuan He, Serkan Araci, Hari M. Srivastava, Mehmet Açikgöz
- Applied Mathematics and Computation
- 2015

- Mehmet Açikgöz, Dilek Erdal, Serkan Araci, Claudio Cuevas
- 2011

Copyright q 2010 Mehmet Açikgöz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We present a new generating function related to the q-Bernoulli numbers and q-Bernoulli polynomials. We… (More)

- SERKAN ARACI, MEHMET ACIKGOZ, HASSAN JOLANY, Kurt Hensel, H. JOLANY
- 2012

In the present paper, we introduce modified Dirichlet's type of twisted q-Euler poly-nomials with weight α. We apply the method of generating function and p-adic q-integral representation on Z p , which are exploited to derive further classes of q-Euler numbers and polynomials. Our new generating function possess a number of interesting properties which we… (More)

- Serkan Araci, Mehmet Açikgöz, Erdogan Sen
- Applied Mathematics and Computation
- 2014

Keywords: Genocchi numbers and polynomials q-Genocchi numbers von Staudt–Clausen's theorem Kummer congruence a b s t r a c t Recently, the von Staudt–Clausen's theorem for q-Euler numbers was introduced by Kim (2013) and q-Genocchi numbers were constructed by Araci et al. (2013). In this paper, we give the corresponding von Staudt–Clausen's theorem for… (More)

- Serkan Araci
- Applied Mathematics and Computation
- 2014

In the present paper, we introduce Eulerian polynomials with parameters a and b and give the definition of them. By using the definition of generating function for our polynomials, we derive some new identities in Analytic Numbers Theory. Also, we give relations between Eulerian polynomials with parameters a and b, Bernstein polynomials, Poly-logarithm… (More)

- SERKAN ARACI, MEHMET ACIKGOZ, KYOUNG-HO PARK, HASSAN JOLANY, Kurt Hensel
- 2012

The present paper deals with uni…cation of the multiple twisted Euler and Genocchi numbers and polynomials associated with p-adic q-integral on Zp at q = 1. Some earlier results of Ozden's papers in terms of uni…ca-tion of the multiple twisted Euler and Genocchi numbers and polynomials associated with p-adic q-integral on Zp at q = 1 can be deduced. We… (More)

- Mehmet Açikgöz, Serkan Araci, Ismail Naci Cangül
- Applied Mathematics and Computation
- 2011

- Sheetal Deshwal, P N Agrawal, Serkan Araci
- Journal of inequalities and applications
- 2017

In this paper, we construct a sequence of modified Stancu-Baskakov operators for a real valued function bounded on [Formula: see text], based on a function [Formula: see text]. This function [Formula: see text] is infinite times continuously differentiable on [Formula: see text] and satisfy the conditions [Formula: see text] and [Formula: see text] is… (More)

- Serkan Araci, Waseem A. Khan, Mehmet Acikgoz, Cenap Özel, Poom Kumam
- SpringerPlus
- 2016

By using the modified Milne-Thomson's polynomial given in Araci et al. (Appl Math Inf Sci 8(6):2803-2808, 2014), we introduce a new concept of the Apostol Hermite-Genocchi polynomials. We also perform a further investigation for aforementioned polynomial and derive some implicit summation formulae and general symmetric identities arising from different… (More)