150 citations · 305 across the 41 of their papers we have counts for
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The Evaluation of the Sums of More General Series by Bernstein Polynomials
Mehmet Acikgoz, Ilknur Koca, Serkan Araci
Let n,k be the positive integers, and let S_{k}(n) be the sums of the k-th power of positive integers up to n. By means of that we consider the evaluation of the sum of more genera…
The Legendre polynomials associated with Bernoulli, Euler, Hermite and Bernstein polynomials
Serkan Araci, Mehmet Acikgoz, Armen Bagdasaryan +1
In the present paper, we deal mainly with arithmetic properties of Legendre polynomials by using their orthogonality property. We show that Legendre polynomials are proportional wi…
Some New Symmetric Identities for the q-Zeta Type Functions
Serkan Araci, Armen Bagdasaryan, Cenap Ozel +1
The main object of this paper is to obtain several symmetric properties of the q-Zeta type functions. As applications of these properties, we give some new interesting identities f…
Extended fermionic -adic integrals on
Feng Qi, Serkan Araci, Mehmet Acikgoz
In the paper, using the extended fermionic -adic integral on , the authors find some applications of the umbral calculus. From these applications, the authors deri…
Identities involving the -Genocchi polynomials and -Zeta-type function
Armen Bagdasaryan, Erdogan Sen, Yuan He +2
The fundamental objective of this paper is to obtain some interesting properties for -Genocchi numbers and polynomials by using the fermionic -adic -integra…
On the modified q-Genocchi numbers and polynomials and their applications
Serkan Araci, Armen Bagdasaryan, Erkan Agyuz +1
The main objective of this paper is to introduce the modified q-Genocchi polynomials and to define their generating function. In the paper, we show new relations, which are explici…
Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis
Armen Bagdasaryan, Serkan Araci, Mehmet Acikgoz +1
In the present paper, we obtain new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived using a Bernoulli polynomial basis.…
p-adic interpolation function related to multiple generalized Genocchi numbers
Serkan Araci, Mehmet Acikgoz, Erdoğan Şen
In the present paper, we deal with multiple generalized Genocchi numbers and polynomials. Also, we introduce analytic interpolating function for the multiple generalized Genocchi n…
A note on the q-Dedekind-type Daehee-Changhee sums with weight alpha arising from modified q-Genocchi polynomials with weight alpha
Serkan Araci, Mehmet Acikgoz, Ayhan Esi
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 co…
Extended q-Dedekind-type Daehee-Changhee sums associated with Extended q-Euler polynomials
Serkan Araci, Mehmet Acikgoz
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…
Extended Fermionic p-Adic q-Integrals On Zp In Connection With Applications Of Umbral Calculus
Serkan Araci, Mehmet Acikgoz, Erdoğan Şen
The purpose of this paper is to derive some applications of umbral calculus by using extended fermionic p-adic q-integral on Zp. From those applications, we derive some new interes…
A New Approach to Multivariate q-Euler polynomials by using Umbral calculus
Serkan Araci, Xiangxing Kong, Mehmet Acikgoz +1
In this work, we derive numerous identities for multivariate q-Euler polynomials by using umbral calculus.
Identities involving q-Genocchi numbers and polynomials
Serkan Araci, Mehmet Acikgoz, Hassan Jolany +1
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 integra…
Some New Identities of Genocchi Numbers and Polynomials involving Bernoulli and Euler polynomials
Serkan Araci, Mehmet Acikgoz, Erdoğan Şen
In this paper, we will deal with some new formulae for two product Genocchi polynomials together with both Euler polynomials and Bernoulli polynomials. We get some applications for…
Dirichlet's type of twisted Eulerian polynomials in connection with Eulerian-L-function
Serkan Araci, Mehmet Acikgoz
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 intere…
New Generalization of Eulerian polynomials and their applications
Serkan Araci, Mehmet Acikgoz, Erdoğan Şen
In the present paper, we introduce Eulerian polynomials with a and b parameters and give the definition of them. By using the definition of generating function for our polynomials,…
On the Dirichlet's type of Eulerian polynomials
Serkan Araci, Mehmet Acikgoz, Deyao Gao
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 Diri…
Some New Identities on the (h,q)-Genocchi numbers and polynomials with weight alpha
Serkan Araci, Elif Cetin, Mehmet Acikgoz +1
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.
On the families of q-Euler numbers and polynomials and their applications
Serkan Araci, Mehmet Acikgoz, Hassan Jolany
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 de…
A note on the (h,q)-Zeta type function with weight alpha
E. Cetin, M. Acikgoz, I. N. Cangul +1
The objective of this paper is to derive symmetric property of (h,q)-Zeta function with weight alpha. By using this property, we give some interesting identities for (h,q)-Genocchi…
The Frobenius-Euler function and its applications
Serkan Araci, Deyao Gao, Mehmet Acikgoz
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 interest…
On the q-Hardy-Littlewood-type maximal operator with weight related to fermionic p-adic q-integral on Zp
Serkan Araci, Mehmet Acikgoz
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…
A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials
Serkan Araci, Mehmet Acikgoz
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 representat…
A new approach to modified q-Bernstein polynomials for functions of two variables with their generating and interpolation functions
Mehmet Acikgoz, Serkan Araci
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 a…