# Korovkin-type results on convergence of sequences of positive linear maps on function spaces

## TL;DR

This paper extends Korovkin-type theorems to the convergence of positive linear maps on function spaces, even when the limit is not necessarily linear, with new generalizations and examples.

## Contribution

It introduces generalized Korovkin-type results for positive linear maps converging to possibly non-linear isometries on continuous function spaces.

## Key findings

- Established new convergence criteria for positive linear maps.
- Provided illustrative examples demonstrating the generalized results.
- Extended classical Korovkin theorems to broader settings.

## Abstract

In this paper we deal with the convergence of sequences of positive linear maps to a (not assumed to be linear) isometry on spaces of continuous functions. We obtain generalizations of known Korovkin-type results and provide several illustrative examples.