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

2023/07/05 by Listán-García, M. del Carmen, de la Rosa, María Pilar Romero
#40A35 #40H05 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2307.02515

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.

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