Higher Order Approximation of Functions by Modified Goodman-Sharma Operators

TL;DR

This paper investigates a modified Goodman-Sharma operator that offers higher order approximation of functions, providing theoretical results including direct and strong converse theorems based on K-functionals.

Contribution

It introduces a new modified Goodman-Sharma operator that improves approximation order and establishes its theoretical approximation properties.

Findings

The modified operator achieves higher approximation order than the original.

The paper proves direct and converse theorems using K-functionals.

The operator is linear but not positive, offering unique approximation advantages.

Abstract

Here we study the approximation properties of a modified Goodman-Sharma operator recently considered by Acu and Agrawal in 2019. This operator is linear but not positive. It has the advantage of a higher order of approximation of functions compared with the Goodman-Sharma operator. We prove direct and strong converse theorems in terms of a related K-functional.