Nonlinear versions of Korovkin's abstract theorems

TL;DR

This paper extends Korovkin's theorems to nonlinear operators that are sublinear, monotone, and weakly additive on function spaces, broadening the scope of approximation theory.

Contribution

It introduces nonlinear versions of Korovkin's theorems for specific classes of operators on continuous function spaces, with illustrative examples.

Findings

Established Korovkin-type approximation theorems for nonlinear operators.

Provided examples demonstrating the applicability of the theorems.

Extended classical results to broader classes of operators.

Abstract

In this paper we prove Korovkin type theorems for sequences of sublinear, monotone and weak additive operators acting on function spaces C(X); where X is a compact or a locally compact metric space. Our results are illustrated by a series of examples