IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v56y2025i4d10.1007_s13226-024-00616-1.html
   My bibliography  Save this article

An inertial parallel iterative method for solving generalized mixed equilibrium problems and common fixed point problem in reflexive Banach spaces

Author

Listed:
  • Nguyen Trung Hieu

    (Dong Thap University)

  • Nguyen Dung

    (Dong Thap University)

Abstract

By combining the shrinking projection method with the parallel splitting-up technique and the inertial term, we introduce a new inertial parallel iterative method for finding common solutions of a finite system of generalized mixed equilibrium problems and common fixed points of a finite family of Bregman totally quasi-asymptotically nonexpansive mappings. After that, we prove a strong convergence result for the proposed iteration in reflexive Banach spaces. By this theorem, we obtain some convergence results for generalized mixed equilibrium problems in reflexive Banach spaces. In addition, we give a numerical example to illustrate the proposed iterations. The obtained results are improvements and extensions to some known results in this area.

Suggested Citation

  • Nguyen Trung Hieu & Nguyen Dung, 2025. "An inertial parallel iterative method for solving generalized mixed equilibrium problems and common fixed point problem in reflexive Banach spaces," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(4), pages 1398-1415, December.
    • Handle: RePEc:spr:indpam:v:56:y:2025:i:4:d:10.1007_s13226-024-00616-1
    DOI: 10.1007/s13226-024-00616-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-024-00616-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13226-024-00616-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    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:spr:indpam:v:56:y:2025:i:4:d:10.1007_s13226-024-00616-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.