Some Fuzzy Korovkin type Approximation Theorems via Power Series Summability Method

TL;DR

This paper introduces a new Korovkin type approximation theorem for fuzzy sequences of positive linear operators using power series summability, enhancing convergence analysis with fuzzy modulus of smoothness and demonstrating advantages over previous results.

Contribution

It presents a novel power series summability based Korovkin approximation theorem for fuzzy operators, extending classical results with fuzzy modulus of smoothness and an illustrative example.

Findings

New summability-based Korovkin theorem for fuzzy operators

Enhanced convergence rate analysis using fuzzy modulus of smoothness

Illustration of advantages over previous fuzzy Korovkin theorems

Abstract

This article provides a power series summability based Korovkin type approximation theorem for any fuzzy sequence of positive linear operators. Using the notion of fuzzy modulus of smoothness, we also derive an associated approximation theorem concerning the fuzzy rate of convergence of these operators. Furthermore, through an example, we illustrate that our summability based Korovin type theorem is an advantage over the fuzzy Korovkin type theorem proved in the seminal paper by Anastassiou (Stud. Univ. Babe\c{s}-Bolyai Math. 4 (2005), 3--10).