Strong Converse Inequalities for Bernstein Operators via Krawtchouk Polynomials

Abstract

We obtain strong converse inequalities for the Bernstein operators with explicit constants. One of the main ingredients in our approach is the representation of the derivatives of the Bernstein operators in terms of the orthogonal polynomials with respect to the binomial distribution, namely, the Krawtchouk polynomials

We found an error in Lemma 4, namely, the factor m! is missed in formula (32). This implies that the results given in Section 4 are wrong, and therefore the proof of our main result is also wrong