Strong Converse Inequalities for Bernstein Operators via Krawtchouk Polynomials

TL;DR

This paper establishes strong converse inequalities for Bernstein operators using Krawtchouk polynomials, providing explicit constants and a novel representation of derivatives in terms of orthogonal polynomials.

Contribution

It introduces a new approach to derive strong converse inequalities for Bernstein operators utilizing Krawtchouk polynomials and explicit derivative representations.

Findings

Derived strong converse inequalities with explicit constants.

Represented derivatives of Bernstein operators via Krawtchouk polynomials.

Enhanced understanding of approximation properties of Bernstein operators.

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