Pointwise weighted approximation of functions with endpoint singularities by combinations of Bernstein operators

TL;DR

This paper develops new theoretical results on how well functions with endpoint singularities can be approximated using combinations of Bernstein operators, considering weights.

Contribution

It provides direct and inverse theorems for weighted approximation of functions with endpoint singularities using Bernstein operator combinations, advancing approximation theory.

Findings

Established new direct theorems for weighted approximation.

Proved inverse theorems characterizing approximation quality.

Extended Bernstein operator theory to functions with endpoint singularities.

Abstract

We give direct and inverse theorems for the weighted approximation of functions with endpoint singularities by combinations of Bernstein operators.