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Statistical Blending-Type Approximation by a Class of Operators That Includes Shape Parameters λ and α

Author

Listed:
  • Qing-Bo Cai

    (Fujian Provincial Key Laboratory of Data-Intensive Computing, Key Laboratory of Intelligent Computing and Information Processing, 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)

  • Merve Temizer Ersoy

    (Department of Software Engineering, Faculty of Engineering and Architecture, Nisantasi University, Istanbul 34398, Turkey)

  • Faruk Özger

    (Department of Engineering Sciences, İzmir Katip Çelebi University, İzmir 35620, Turkey)

Abstract

This paper is devoted to studying the statistical approximation properties of a sequence of univariate and bivariate blending-type Bernstein operators that includes shape parameters α and λ and a positive integer. An estimate of the corresponding rates was obtained, and a Voronovskaja-type theorem is given by a weighted A -statistical convergence. A Korovkin-type theorem is provided for the univariate and bivariate cases of the blending-type operators. Moreover, the convergence behavior of the univariate and bivariate new blending basis and new blending operators are exhaustively demonstrated by computer graphics. The studied univariate and bivariate blending-type operators reduce to the well-known Bernstein operators in the literature for the special cases of shape parameters α and λ , and they propose better approximation results.

Suggested Citation

  • Qing-Bo Cai & Khursheed J. Ansari & Merve Temizer Ersoy & Faruk Özger, 2022. "Statistical Blending-Type Approximation by a Class of Operators That Includes Shape Parameters λ and α," Mathematics, MDPI, vol. 10(7), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1149-:d:786019
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    References listed on IDEAS

    as
    1. Hari M. Srivastava & Khursheed J. Ansari & Faruk Özger & Zeynep Ödemiş Özger, 2021. "A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices," Mathematics, MDPI, vol. 9(16), pages 1-15, August.
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    Cited by:

    1. Faruk Özger & Ekrem Aljimi & Merve Temizer Ersoy, 2022. "Rate of Weighted Statistical Convergence for Generalized Blending-Type Bernstein-Kantorovich Operators," Mathematics, MDPI, vol. 10(12), pages 1-21, June.

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