Estimates for the differences of positive linear operators and their derivatives

TL;DR

This paper provides quantitative estimates for the differences between various positive linear operators and their derivatives, using modulus of continuity, with numerical examples illustrating the theoretical results.

Contribution

It introduces new estimates for differences of positive linear operators and their derivatives, applicable to operators like Bernstein and Kantorovich, with a focus on bounded intervals.

Findings

Derived estimates in terms of first modulus of continuity.

Applied results to operators such as Bernstein and Durrmeyer.

Included numerical examples demonstrating theoretical findings.

Abstract

The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Our approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine Bernstein-Durrmeyer operators, Durrmeyer operators with Jacobi weights. The estimates in quantitative form are given in terms of first modulus of continuity. In order to analyze the theoretical results in the last section we consider some numerical examples.