Another weighted approximation of functions with singularities by combinations of Bernstein operators

TL;DR

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

Contribution

It presents a novel combination of Bernstein operators tailored for better approximation of singular functions, expanding on previous methods.

Findings

New combination of Bernstein operators effectively approximates singular functions.

Established direct and inverse weighted approximation theorems.

Demonstrated improved approximation properties over existing methods.

Abstract

A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new type combinations are given.