Asymptotic and Non-asymptotic Results in the Approximation by Bernstein Polynomials

摘要

This paper deals with the approximation of functions by the classical Bernstein polynomials in terms of the Ditzian-Totik modulus of smoothness. Asymptotic and non-asymptotic results are respectively stated for continuous and twice continuously differentiable functions. By using a probabilistic approach, known results are either completed or strengthened.