IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i12p1161-d293114.html
   My bibliography  Save this article

Bivariate α , q -Bernstein–Kantorovich Operators and GBS Operators of Bivariate α , q -Bernstein–Kantorovich Type

Author

Listed:
  • Qing-Bo Cai

    (School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China)

  • Wen-Tao Cheng

    (School of Mathematics and Computation Sciences, Anqing Normal University, Anhui 246133, China)

  • Bayram Çekim

    (Department of Mathematics, Faculty of Science, Gazi University, Beşevler, Ankara 06500, Turkey)

Abstract

In this paper, we introduce a family of bivariate α , q -Bernstein–Kantorovich operators and a family of G B S (Generalized Boolean Sum) operators of bivariate α , q -Bernstein–Kantorovich type. For the former, we obtain the estimate of moments and central moments, investigate the degree of approximation for these bivariate operators in terms of the partial moduli of continuity and Peetre’s K -functional. For the latter, we estimate the rate of convergence of these G B S operators for B -continuous and B -differentiable functions by using the mixed modulus of smoothness.

Suggested Citation

  • Qing-Bo Cai & Wen-Tao Cheng & Bayram Çekim, 2019. "Bivariate α , q -Bernstein–Kantorovich Operators and GBS Operators of Bivariate α , q -Bernstein–Kantorovich Type," Mathematics, MDPI, vol. 7(12), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1161-:d:293114
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/12/1161/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/12/1161/
    Download Restriction: no
    ---><---

    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:7:y:2019:i:12:p:1161-:d:293114. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.