Some identities for q-Bernoulli numbers and polynomials arising from q-Bernstein polynomials

Abstract

In this paper, we study q-Bernoulli numbers and polynomials which are different from Garlitz q-Bernoulli numbers and polynomials and arising from p-adic invariant integrals on Zp, and investigate some properties of these numbers and polynomials. Then we will consider p-adic invariant integrals on Zp of the g-Bernstein polynomials and show that they can be expressed in terms of the q-Bernoulli numbers. In addition, from such p-adic invariant integrals we will derive some identities for the q-Bernoulli numbers. ? 2018 Advanced Studies in Contemporary Mathematics (Kyungshang). All rights reserved.