IDEAS home Printed from https://ideas.repec.org/a/hin/jnddns/8432560.html
   My bibliography  Save this article

Convergence Analysis of an Iteration Process for a Class of Generalized Nonexpansive Mappings with Application to Fractional Differential Equations

Author

Listed:
  • Kifayat Ullah
  • Sabri T. M. Thabet
  • Anwar Kamal
  • Junaid Ahmad
  • Fayyaz Ahmad
  • Rigoberto Medina

Abstract

We consider the class of generalized α-nonexpansive mappings in a setting of Banach spaces. We prove existence of fixed point and convergence results for these mappings under the K∗-iterative process. The weak convergence is obtained with the help of Opial’s property while strong convergence results are obtained under various assumptions. Finally, we construct two numerical examples and connect our K∗-iterative process with them. An application to solve a fractional differential equation (FDE) is also provided. It has been eventually shown that the K∗- iterative process of this example gives more accurate numerical results corresponding to some other iterative processes of the literature. The main outcome is new and improves some known results of the literature.

Suggested Citation

  • Kifayat Ullah & Sabri T. M. Thabet & Anwar Kamal & Junaid Ahmad & Fayyaz Ahmad & Rigoberto Medina, 2023. "Convergence Analysis of an Iteration Process for a Class of Generalized Nonexpansive Mappings with Application to Fractional Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2023, pages 1-9, March.
    • Handle: RePEc:hin:jnddns:8432560
    DOI: 10.1155/2023/8432560
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/ddns/2023/8432560.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/ddns/2023/8432560.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2023/8432560?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
    ---><---

    More about this item

    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:hin:jnddns:8432560. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.