IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i10p1678-d815105.html
   My bibliography  Save this article

A Mean Convergence Theorem without Convexity for Finite Commutative Nonlinear Mappings in Reflexive Banach Spaces

Author

Listed:
  • Lawal Yusuf Haruna

    (Department of Mathematical Sciences, Kaduna State University, Kaduna P.M.B. 2339, Nigeria
    These authors contributed equally to this work.)

  • Bashir Ali

    (Department of Mathematical Sciences, Bayero University, Kano 700006, Nigeria
    These authors contributed equally to this work.)

  • Yekini Shehu

    (College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
    These authors contributed equally to this work.)

  • Jen-Chih Yao

    (Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
    These authors contributed equally to this work.)

Abstract

This paper investigates the Bregman version of the Takahashi-type generic 2-generalized nonspreading mapping which includes the generic 2-generalized Bregman nonspreading mapping as a special case. Relative to the attractive points of nonlinear mapping, the Baillon-type nonlinear mean convergence theorem for finite commutative generic 2-generalized Bregman nonspreading mappings without the convexity assumption is proved in the setting of reflexive Banach spaces. Using this result, some new and well-known nonlinear mean convergence theorems for the finite generic generalized Bregman nonspreading mapping, the 2-generalized Bregman nonspreading mapping and the normally 2-generalized hybrid mapping, among others, are established. Our results extend and generalize many corresponding ones announced in the literature.

Suggested Citation

  • Lawal Yusuf Haruna & Bashir Ali & Yekini Shehu & Jen-Chih Yao, 2022. "A Mean Convergence Theorem without Convexity for Finite Commutative Nonlinear Mappings in Reflexive Banach Spaces," Mathematics, MDPI, vol. 10(10), pages 1-20, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1678-:d:815105
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/10/1678/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/10/1678/
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:10:p:1678-:d:815105. 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.