Approximation properties of modified Sz\'{a}sz-Mirakyan operators in polynomial weighted space

TL;DR

This paper introduces modified Szász-Mirakyan operators within polynomial weighted spaces and investigates their approximation properties, expanding understanding of their effectiveness in function approximation.

Contribution

The paper presents new modified Szász-Mirakyan operators and analyzes their approximation capabilities in polynomial weighted spaces, a novel approach in this context.

Findings

Operators effectively approximate functions in weighted spaces

Established convergence properties of the modified operators

Provided theoretical bounds for approximation errors

Abstract

We introduce certain modified Sz\'{a}sz-Mirakyan operators in polynomial weighted spaces of functions of one variable. We studied approximation properties of these operators.