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

Author

Listed:
  • Qing-Bo Cai

    (School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China
    These authors contributed equally to this work.)

  • Khursheed J. Ansari

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
    These authors contributed equally to this work.)

  • Fuat Usta

    (Department of Mathematics, Faculty of Arts and Sciences, Düzce University, Düzce 81620, Turkey
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Qing-Bo Cai & Khursheed J. Ansari & Fuat Usta, 2021. "A Note on New Construction of Meyer-König and Zeller Operators and Its Approximation Properties," Mathematics, MDPI, vol. 9(24), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3275-:d:704180
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