Convergence of the Bernstein-Durrmeyer operators in variation seminorm

TL;DR

This paper investigates the convergence and variation-detracting properties of Bernstein-Durrmeyer operators in the space of functions with bounded variation, including their approximation rates.

Contribution

It provides new insights into the variation convergence and approximation rates of Bernstein-Durrmeyer operators in bounded variation spaces.

Findings

Proved convergence of Bernstein-Durrmeyer operators in variation seminorm.

Established variation detracting properties of these operators.

Analyzed the rate of approximation in the variation seminorm.

Abstract

The aim of this paper is to study variation detracting property and con- vergence in variation of the Bernstein-Durrmeyer modifications of the classical Bernstein operators in the space of functions of bounded variation. These problems are studied with respect to the variation seminorm. Moreover we also study the problem of the rate of approximation.