Direct and inverse theorems for Bernstein operators with inner singularities

TL;DR

This paper introduces a new type of Bernstein operators designed to approximate functions with inner singularities, providing direct and inverse approximation results for these operators.

Contribution

The paper presents a novel Bernstein operator variant capable of handling inner singularities, expanding the scope of approximation theory.

Findings

Established direct approximation results for the new operators.

Proved inverse theorems relating approximation quality to function smoothness.

Demonstrated effectiveness in approximating functions with inner singularities.

Abstract

We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.