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On One- and Two-Dimensional α –Stancu–Schurer–Kantorovich Operators and Their Approximation Properties

Author

Listed:
  • Md. Heshamuddin

    (Department of Natural & Applied Sciences, Glocal University, Saharanpur-247121, Uttar Pradesh, India)

  • Nadeem Rao

    (Department of Applied Sciences & Humanities, Panipat Institute of Engineering and Technology, Pattikalyana, Samalkha, Panipat-132102, Haryana, India)

  • Bishnu P. Lamichhane

    (School of Information & Physical Sciences, The University of Newcastle, University Drive, Callaghan, NSW 2308, Australia)

  • Adem Kiliçman

    (Department of Mathematics & Statistics, Faculty of Science, Universiti Putra Malaysia, UPM Serdang 43400, Selangor, Malaysia)

  • Mohammad Ayman-Mursaleen

    (School of Information & Physical Sciences, The University of Newcastle, University Drive, Callaghan, NSW 2308, Australia
    Department of Mathematics & Statistics, Faculty of Science, Universiti Putra Malaysia, UPM Serdang 43400, Selangor, Malaysia)

Abstract

The goal of this research article is to introduce a sequence of α –Stancu–Schurer–Kantorovich operators. We calculate moments and central moments and find the order of approximation with the aid of modulus of continuity. A Voronovskaja-type approximation result is also proven. Next, error analysis and convergence of the operators for certain functions are presented numerically and graphically. Furthermore, two-dimensional α –Stancu–Schurer–Kantorovich operators are constructed and their rate of convergence, graphical representation of approximation and numerical error estimates are presented.

Suggested Citation

  • Md. Heshamuddin & Nadeem Rao & Bishnu P. Lamichhane & Adem Kiliçman & Mohammad Ayman-Mursaleen, 2022. "On One- and Two-Dimensional α –Stancu–Schurer–Kantorovich Operators and Their Approximation Properties," Mathematics, MDPI, vol. 10(18), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3227-:d:907814
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    References listed on IDEAS

    as
    1. Adem Kilicman & Mohammad Ayman Mursaleen & Ahmed Ahmed Hussin Ali Al-Abied, 2020. "Stancu Type Baskakov—Durrmeyer Operators and Approximation Properties," Mathematics, MDPI, vol. 8(7), pages 1-13, July.
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