A Note on New Construction of Meyer-König and Zeller Operators and Its Approximation Properties

Qing-Bo Cai, Khursheed J. Ansari and Fuat Usta
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Qing-Bo Cai: School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China
Khursheed J. Ansari: Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Fuat Usta: Department of Mathematics, Faculty of Arts and Sciences, Düzce University, Düzce 81620, Turkey

Mathematics, 2021, vol. 9, issue 24, 1-16

Abstract: The topic of approximation with positive linear operators in contemporary functional analysis and theory of functions has emerged in the last century. One of these operators is Meyer–König and Zeller operators and in this study a generalization of Meyer–König and Zeller type operators based on a function τ by using two sequences of functions will be presented. The most significant point is that the newly introduced operator preserves { 1 , τ , τ 2 } instead of classical Korovkin test functions. Then asymptotic type formula, quantitative results, and local approximation properties of the introduced operators are given. Finally a numerical example performed by MATLAB is given to visualize the provided theoretical results.

Keywords: Meyer–König and Zeller operators; modulus of continuity; shape preserving approximation; Voronovskaya theorem; Korovkin type theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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