Pointwise weighted approximation of functions with inner singularities by Bernstein operators

Abstract

We consider the pointwise weighted approximation by Bernstein operators with inner singularities. The related weight functions are weights ¯ w(x) = |x − ξ|α(0 < ξ < 1, α > 0). In this paper we give direct and inverse results of this type of Bernstein polynomials.