On p-Adic Analogue of q-Bernstein Polynomials and Related Integrals

الملخص EN

Recently, Kim's work (in press) introduced q-Bernstein polynomials which are different Phillips' q-Bernstein polynomials introduced in the work by (Phillips, 1996; 1997).

The purpose of this paper is to study some properties of several type Kim's q-Bernstein polynomials to express the p-adic q-integral of these polynomials on ℤp associated with Carlitz's q-Bernoulli numbers and polynomials.

Finally, we also derive some relations on the p-adic q-integral of the products of several type Kim's q-Bernstein polynomials and the powers of them on ℤp.