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

TL;DR

This paper presents a new combination of Bernstein operators designed to improve the approximation of functions with inner singularities, providing both direct and inverse weighted approximation results.

Contribution

Introduction of a novel combination of Bernstein operators specifically for approximating functions with inner singularities, along with theoretical approximation results.

Findings

New combination of Bernstein operators effectively approximates functions with inner singularities

Established direct and inverse weighted approximation theorems for the new operators

Enhances understanding of approximation behavior near singularities

Abstract

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