Abstract. We prove two identities for multivariate Bernstein polynomials on simplex, which are considered on a pointwise. In this paper, we study good approximations of Bernstein polynomials for every continuous functions on simplex and the higher dimensional q-analogues of Bernstein polynomials on simplex.
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.
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