Fractional approximation by Bernstein operators

Abstract

We estimate the fractal approximation rate for approximation by Bernstein operators by using the Ditzian-Totik type modulus of continuity. Our results improve the previous theorem of Anastassiou. In the proof, the equivalence  between the K-functional and the Ditzian-Totik type modulus, and the absolute moment estimates with fractal order play important roles.