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 $\bar{w}(x)=|x-\xi|^\alpha(0<\xi<1,\ \alpha>0).$ In this paper we give direct and inverse results of this type of Bernstein polynomials.