On the properties of q-Bernstein-type polynomials

Abstract

The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions depend on the several variables. We derive the recurrence formulas related to the second Stirling numbers and generalized Bernoulli polynomials. Moreover, the interpolation function of these polynomials depend on the several variables and the derivatives of these polynomials and also their generating function are given. Final part of this paper, we get new interesting identities of modified q-Bernoulli numbers and q-Euler numbers applying p-adic q-integral representation on ?p and p-adic fermionic q-invariant integral on ?p, respectively, to the inverse of q-Bernstein polynomials. © 2017 NSP Natural Sciences Publishing Cor.