Approximation by q-Szasz operators

TL;DR

This paper introduces a new q-generalization of Szász operators for q>1, providing convergence estimates and a Voronovskaja-type theorem, showing faster approximation rates than classical operators.

Contribution

It defines and analyzes the approximation properties of q-Szász operators for q>1, including convergence rates and asymptotic behavior, extending classical results.

Findings

Rate of approximation is of order q^{-n} for q>1

Provides quantitative estimates of convergence in weighted spaces

Establishes a Voronovskaja-type theorem for q-Szász operators

Abstract

his paper deals with approximating properties of the newly defined $q$-generalization of the Sz\'{a}sz operators in the case $q>1$. Quantitative estimates of the convergence in the polynomial weighted spaces and the Voronovskaja's theorem are given. In particular, it is proved that the rate of approximation by the $q$-Sz\'{a}sz operators ($q>1$) is of order $q^{-n}$ versus $1/n$ for the classical Sz\'{a}sz--Mirakjan operators.