IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i7p1149-d786019.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/7/1149/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/7/1149/
    Download Restriction: no
    ---><---

    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.
    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. 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.

    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. 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.
    2. Hari Mohan Srivastava, 2022. "Higher Transcendental Functions and Their Multi-Disciplinary Applications," Mathematics, MDPI, vol. 10(24), pages 1-3, December.
    3. 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.

    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:7:p:1149-:d:786019. 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.