Korovkin-type approximation results through summability methods in the Applied Science

TL;DR

This paper develops Korovkin approximation theorems using summability methods, unifying previous results and introducing new theorems for various convergence methods, with insights into their structural properties.

Contribution

It provides a unified framework for Korovkin approximation theorems via summability methods, including new results for regular matrix convergence and convergence through ideals.

Findings

Unified treatment of Korovkin approximation via summability methods

New results for regular matrix convergence methods

Insights into properties needed for summability methods

Abstract

We present Korovkin approximation theorems that incorporate summability methods. These result allows us to obtain a unified treatment of several previous results, focusing on the underlying structure and the properties that a summability method should satisfy in order to establish a Korovkin-type approximation result. As a by-product we obtain new Korovkin-type results incorporating summability methods, for example for regular matrix convergence methods, convergence through ideals of natural numbers, etc, and we provide further directions and a preparation for questions which remain open.