IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i16p1942-d614386.html
   My bibliography  Save this article

Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications

Author

Listed:
  • Ioannis K. Argyros

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

Abstract

A plethora of sufficient convergence criteria has been provided for single-step iterative methods to solve Banach space valued operator equations. However, an interesting question remains unanswered: is it possible to provide unified convergence criteria for single-step iterative methods, which are weaker than earlier ones without additional hypotheses? The answer is yes. In particular, we provide only one sufficient convergence criterion suitable for single-step methods. Moreover, we also give a finer convergence analysis. Numerical experiments involving boundary value problems and Hammerstein-like integral equations complete this paper.

Suggested Citation

  • Ioannis K. Argyros, 2021. "Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications," Mathematics, MDPI, vol. 9(16), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1942-:d:614386
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/16/1942/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/16/1942/
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Janak Raj Sharma & Harmandeep Singh & Ioannis K. Argyros, 2022. "A Unified Local-Semilocal Convergence Analysis of Efficient Higher Order Iterative Methods in Banach Spaces," Mathematics, MDPI, vol. 10(17), pages 1-16, September.
    2. Ioannis K. Argyros & Samundra Regmi & Stepan Shakhno & Halyna Yarmola, 2022. "A Methodology for Obtaining the Different Convergence Orders of Numerical Method under Weaker Conditions," Mathematics, MDPI, vol. 10(16), pages 1-16, August.
    3. Ioannis K. Argyros & Christopher Argyros & Johan Ceballos & Daniel González, 2022. "Extended Comparative Study between Newton’s and Steffensen-like Methods with Applications," Mathematics, MDPI, vol. 10(16), pages 1-12, August.
    4. Samundra Regmi & Ioannis K. Argyros & Santhosh George & Michael I. Argyros, 2022. "A Comparison Study of the Classical and Modern Results of Semi-Local Convergence of Newton–Kantorovich Iterations-II," Mathematics, MDPI, vol. 10(11), pages 1-12, May.
    5. Manoj K. Singh & Ioannis K. Argyros, 2022. "The Dynamics of a Continuous Newton-like Method," Mathematics, MDPI, vol. 10(19), pages 1-14, October.
    6. Michael I. Argyros & Ioannis K. Argyros & Samundra Regmi & Santhosh George, 2022. "Generalized Three-Step Numerical Methods for Solving Equations in Banach Spaces," Mathematics, MDPI, vol. 10(15), pages 1-28, July.
    7. Santhosh George & Jidesh Padikkal & Krishnendu Remesh & Ioannis K. Argyros, 2022. "A New Parameter Choice Strategy for Lavrentiev Regularization Method for Nonlinear Ill-Posed Equations," Mathematics, MDPI, vol. 10(18), pages 1-24, September.
    8. Ramandeep Behl & Ioannis K. Argyros & Fouad Othman Mallawi & Samaher Khalaf Alharbi, 2022. "Extending the Applicability of Highly Efficient Iterative Methods for Nonlinear Equations and Their Applications," Mathematics, MDPI, vol. 11(1), pages 1-18, December.
    9. Samundra Regmi & Ioannis K. Argyros & Santhosh George & Christopher I. Argyros, 2022. "A Comparison Study of the Classical and Modern Results of Semi-Local Convergence of Newton-Kantorovich Iterations," Mathematics, MDPI, vol. 10(8), pages 1-14, April.

    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:9:y:2021:i:16:p:1942-:d:614386. 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.