Identities involving the $\left(h,q\right)$-Genocchi polynomials and $\left(h,q\right)$-Zeta-type function

Abstract

The fundamental objective of this paper is to obtain some interesting properties for (h, q)-Genocchi numbers and polynomials by using the fermionic p-adic q-integral on Zp and mentioned in the paper q-Bernstein polynomials. By considering the q-Euler zeta function defined by T. Kim, which can also be obtained by applying the Mellin transformation to the generating function of (h, q)-Genocchi polynomials, we study (h, q)-Zeta-type function. We derive symmetric properties of (h, q)-Zeta function and from these properties we give symmetric property of (h, q)-Genocchi polynomials.