Generalization of Sz\'{a}sz operators involving multiple Sheffer polynomials

TL;DR

This paper introduces a generalization of Szász operators using multiple Sheffer polynomials, analyzing their convergence and approximation properties with theoretical proofs and specific examples.

Contribution

It presents a novel generalization of Szász operators involving multiple Sheffer polynomials and studies their convergence and approximation behavior.

Findings

Operators converge uniformly on bounded functions

Approximation order is quantified using modulus of continuity

Theoretical results are illustrated with specific polynomial cases

Abstract

The present work deals with the mathematical investigation of some generalizations of the Sz\'{a}sz operators. In this work, the multiple Sheffer polynomials are introduced. The generalization of Sz\'{a}sz operators involving multiple Sheffer polynomials are considered. Convergence properties of these operators are verified with the help of the universal Korovkin-type property and the order of approximation is calculated by using classical modulus of continuity. The theoretical results are exemplified choosing the special cases of multiple Sheffer polynomials.