Approximation by complex Szasz-Durrmeyer-Chlodowsky operators in compact disks

TL;DR

This paper investigates the overconvergence and approximation properties of Szász-Durrmeyer-Chlodowsky operators for analytic functions in compact disks, providing quantitative estimates and asymptotic results.

Contribution

It extends the understanding of overconvergence phenomena for these operators, including exact orders and asymptotic behavior in complex domains.

Findings

Demonstrates overconvergence of the operators in compact disks.

Provides upper estimates and Voronovskaja type results.

Establishes exact order and asymptotic estimates for approximation.

Abstract

In the present article, we deal with the overconvergence of the Sz?asz-Durrmeyer-Chlodowsky operators. Here we study the approximation properties e.g. upper estimates, Voronovskaja type result for these operators attached to analytic functions in compact disks. Also, we discuss the exact order in simultaneous approximation by these operators and its derivatives and the asymptotic result with quantitative upper estimate. In such a way, we put in evidence the overconvergence phenomenon for the Sz?asz-Durrmeyer-Chlodowsky operators, namely the extensions of approximation properties with exact quantitative estimates and orders of these convergencies to sets in the complex plane that contain the interval [0,\infty).