On Generalized Sz\'{a}sz-Mirakyan operators

TL;DR

This paper introduces a generalized class of Szász-Mirakyan operators, providing theoretical results on their approximation properties, asymptotic behavior, and statistical convergence.

Contribution

It extends Szász-Mirakyan operators by incorporating real parameters, offering new theoretical insights into their approximation capabilities.

Findings

Established degree of approximation for the generalized operators

Derived Voronovskaya asymptotic formula

Proved statistical convergence of the operators

Abstract

In the present article, we propose the generalization of Sz\'{a}sz-Mirakyan operators, which is a class of linear positive operators of discrete type depending on a real parameters. We give theorem of degree of approximation, the Voronovskaya Asymptotic formula and statistical convergence.