IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i22p4179-d967089.html
   My bibliography  Save this article

Approximation of the Fixed Point of the Product of Two Operators in Banach Algebras with Applications to Some Functional Equations

Author

Listed:
  • Khaled Ben Amara

    (Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Sfax 3000, Tunisia)

  • Maria Isabel Berenguer

    (Department of Applied Mathematics, E.T.S. de Ingeniería de Edificación, University of Granada, 18071 Granada, Spain
    Institute of Mathematics (IMAG), University of Granada, 18071 Granada, Spain)

  • Aref Jeribi

    (Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Sfax 3000, Tunisia)

Abstract

Making use of the Boyd-Wong fixed point theorem, we establish a new existence and uniqueness result and an approximation process of the fixed point for the product of two nonlinear operators in Banach algebras. This provides an adequate tool for deriving the existence and uniqueness of solutions of two interesting type of nonlinear functional equations in Banach algebras, as well as for developing an approximation method of their solutions. In addition, to illustrate the applicability of our results we give some numerical examples.

Suggested Citation

  • Khaled Ben Amara & Maria Isabel Berenguer & Aref Jeribi, 2022. "Approximation of the Fixed Point of the Product of Two Operators in Banach Algebras with Applications to Some Functional Equations," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4179-:d:967089
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/22/4179/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/22/4179/
    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:10:y:2022:i:22:p:4179-:d:967089. 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.