Nonlinear operator extensions of Korovkin's theorems

TL;DR

This paper extends Korovkin's theorem to sequences of weakly nonlinear and monotone operators on Banach function spaces, providing new theoretical insights and illustrative examples.

Contribution

It introduces nonlinear operator extensions of Korovkin's theorem, expanding its applicability to weakly nonlinear and monotone operators.

Findings

Extended Korovkin's theorem to nonlinear operators

Provided examples illustrating the extended theory

Demonstrated convergence properties in Banach spaces

Abstract

In this paper we extend Korovkin's theorem to the context of sequences of weakly nonlinear and monotone operators defined on certain Banach function spaces. Several examples illustrating the theory are included.