Pointwise Approximation Theorems for Combinations of Bernstein Polynomials With Inner Singularities

TL;DR

This paper develops direct and inverse approximation theorems for functions with inner singularities using combinations of Bernstein polynomials, enhancing understanding of their approximation capabilities.

Contribution

It introduces new approximation theorems specifically for functions with inner singularities using Bernstein polynomial combinations.

Findings

Established direct approximation theorems for weighted functions with singularities.

Proved inverse theorems characterizing approximation quality.

Extended Bernstein polynomial approximation theory to functions with inner singularities.

Abstract

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