IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i13p2145-d1431190.html
   My bibliography  Save this article

Multistep Iterative Methods for Solving Equations in Banach Space

Author

Listed:
  • Ramandeep Behl

    (Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Ioannis K. Argyros

    (Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA)

  • Sattam Alharbi

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia)

  • Hashim Alshehri

    (Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Michael Argyros

    (Computing Sciences and Mathematics, Franklin University, 201 S Grant Ave., Columbus, OH 43215, USA)

Abstract

The novelty of this article lies in the fact that we extend the use of a multistep method for developing a sequence whose limit solves a Banach space-valued equation. We suggest the error estimates, local convergence, and semi-local convergence, a radius of convergence, the uniqueness of the required solution that can be computed under ω -continuity, and conditions on the first derivative, which is on the method. But, earlier studies used high-order derivatives, even though those derivatives do not appear in the body structure of the proposed method. In addition to this, they did not propose computable estimates and semi-local convergence. We checked the applicability of our study to three real-life problems for semi-local convergence and two problems chosen for local convergence. Based on the obtained results, we conclude that our approach improves its applicability and makes it suitable for challenges in applied science.

Suggested Citation

  • Ramandeep Behl & Ioannis K. Argyros & Sattam Alharbi & Hashim Alshehri & Michael Argyros, 2024. "Multistep Iterative Methods for Solving Equations in Banach Space," Mathematics, MDPI, vol. 12(13), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2145-:d:1431190
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/13/2145/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/13/2145/
    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:12:y:2024:i:13:p:2145-:d:1431190. 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.