Korovkin-type Theorems and Approximation by Positive Linear Operators

TL;DR

This survey provides a comprehensive introduction to Korovkin-type theorems, exploring their applications in approximating continuous and L^p-functions with positive linear operators, including new results and a straightforward organization.

Contribution

It offers a detailed, self-contained overview of Korovkin-type theorems with new results and applications, simplifying the understanding of approximation theory.

Findings

New Korovkin-type theorems and applications

Effective approximation of continuous functions

Enhanced understanding of positive linear operators

Abstract

This survey paper contains a detailed self-contained introduction to Korovkin-type theorems and to some of their applications concerning the approximation of continuous functions as well as of L^p-functions, by means of positive linear operators. The paper also contains several new results and applications. Moreover, the organization of the subject follows a simple and direct approach which quickly leads both to the main results of the theory and to some new ones.