Bulletin of the
Korean Mathematical Society BKMS

Recently, T. Kim has introduced and analysed the $q$-Euler polynomials (see [3, 14, 35, 37]). By the same motivation, we will consider some interesting properties of the $q$-Genocchi polynomials. Further, we give some formulae on the Bernstein and $q$-Genocchi polynomials by using $p$-adic integral on $\mathbb Z_p$. From these relationships, we establish some interesting identities.

Keywords: $q$-Genocchi number, $q$-Genocchi polynomial, Bernstein polynomial, $p$-adic integral

MSC numbers: 11S80, 11B68