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A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices

Author

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  • Hari M. Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan
    Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy)

  • Khursheed J. Ansari

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia)

  • Faruk Özger

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

  • Zeynep Ödemiş Özger

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

Abstract

In this study, we present a link between approximation theory and summability methods by constructing bivariate Bernstein-Kantorovich type operators on an extended domain with reparametrized knots. We use a statistical convergence type and power series method to obtain certain Korovkin type theorems, and we study certain rates of convergences related to these summability methods. Furthermore, we numerically analyze the theoretical results and provide some computer graphics to emphasize the importance of this study.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1895-:d:611184
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    References listed on IDEAS

    as
    1. Mursaleen, M. & Ansari, Khursheed J. & Khan, Asif, 2015. "On (p, q)-analogue of Bernstein operators," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 874-882.
    2. Mursaleen, M. & Ansari, Khursheed J. & Khan, Asif, 2016. "Erratum to ``On (p, q)-analogue of Bernstein Operators'' [Appl. Math. Comput. 266 (2015) 874–882]," Applied Mathematics and Computation, Elsevier, vol. 278(C), pages 70-71.
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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.
    2. Francesco Aldo Costabile & Maria Italia Gualtieri & Anna Napoli, 2022. "General Odd and Even Central Factorial Polynomial Sequences," Mathematics, MDPI, vol. 10(6), pages 1-22, March.
    3. Hari Mohan Srivastava, 2022. "Higher Transcendental Functions and Their Multi-Disciplinary Applications," Mathematics, MDPI, vol. 10(24), pages 1-3, December.
    4. 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.

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