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ARTICLE

Approximation by Szász Type Operators Involving Apostol-Genocchi Polynomials

by Mine Menekşe Yılmaz^*

Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, Gaziantep, TR-27310, Turkey

* Corresponding Author: Mine Menekşe Yılmaz. Email:

(This article belongs to the Special Issue: Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)

Computer Modeling in Engineering & Sciences 2022, 130(1), 287-297. https://doi.org/10.32604/cmes.2022.017385

Received 07 May 2021; Accepted 12 July 2021; Issue published 29 November 2021

Abstract

The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of order α. Applying the Korovkin theorem, we arrive at the convergence of the operator with the aid of moments and central moments. We determine the rate of convergence of the operator using several tools such as -functional, modulus of continuity, second modulus of continuity. We also give a type of Voronovskaya theorem for estimating error. Moreover, we investigate some results about convergence properties of the operator in a weighted space. Finally, we give numerical examples to support our theorems by using the Maple.

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