A Note on the Weighted q-Bernoulli Numbers and the Weighted q-Bernstein Polynomials

Recently, the modified q-Bernoulli numbers and polynomials with weight α are introduced in [3]. In this paper we give some interesting p-adic integral representation on Zp of the weighted q-Bernstein polynomials related to the modified q-Bernoulli numbers and polynomials with weight α. From those integral representation on Zp of the weighted q-Bernstein polynomials, we can derive some identities on the modified q-Bernoulli numbers and polynomials with weight α.