IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i12p2027-d836718.html
   My bibliography  Save this article

Rate of Weighted Statistical Convergence for Generalized Blending-Type Bernstein-Kantorovich Operators

Author

Listed:
  • Faruk Özger

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

  • Ekrem Aljimi

    (Faculty of Applied Sciences, Public University “Kadri Zeka”, 60000 Gjilan, Kosovo)

  • Merve Temizer Ersoy

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

Abstract

An alternative approach, known today as the Bernstein polynomials, to the Weierstrass uniform approximation theorem was provided by Bernstein. These basis polynomials have attained increasing momentum, especially in operator theory, integral equations and computer-aided geometric design. Motivated by the improvements of Bernstein polynomials in computational disciplines, we propose a new generalization of Bernstein–Kantorovich operators involving shape parameters λ , α and a positive integer as an original extension of Bernstein–Kantorovich operators. The statistical approximation properties and the statistical rate of convergence are also obtained by means of a regular summability matrix. Using the Lipschitz-type maximal function, the modulus of continuity and modulus of smoothness, certain local approximation results are presented. Some approximation results in a weighted space are also studied. Finally, illustrative graphics that demonstrate the approximation behavior and consistency of the proposed operators are provided by a computer program.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2027-:d:836718
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/12/2027/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/12/2027/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Kadak, Uğur & Braha, Naim L. & Srivastava, H.M., 2017. "Statistical weighted B-summability and its applications to approximation theorems," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 80-96.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Francesco Aldo Costabile & Maria Italia Gualtieri & Anna Napoli, 2022. "Polynomial Sequences and Their Applications," Mathematics, MDPI, vol. 10(24), pages 1-3, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hari Mohan Srivastava & Bidu Bhusan Jena & Susanta Kumar Paikray, 2020. "Statistical Deferred Nörlund Summability and Korovkin-Type Approximation Theorem," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2027-:d:836718. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.