Quantitative estimates of convergence in nonlinear operator extensions of Korovkin's theorems

TL;DR

This paper provides quantitative convergence estimates using the modulus of continuity for nonlinear Korovkin-type theorems involving weakly nonlinear and monotone operators on continuous functions, supported by illustrative examples.

Contribution

It introduces a quantitative approach to convergence in nonlinear Korovkin theorems, extending classical results with explicit estimates.

Findings

Established a modulus of continuity-based convergence estimate

Proved convergence for sequences of weakly nonlinear monotone operators

Provided examples demonstrating the theory's applicability

Abstract

This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of continuous real functions. Several examples illustrating the theory are included.