IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2018i1p31-d194000.html
   My bibliography  Save this article

A Third Order Newton-Like Method and Its Applications

Author

Listed:
  • D. R. Sahu

    (Department of Mathematics, Banaras Hindu University, Varanasi-221005, India)

  • Ravi P. Agarwal

    (Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, USA)

  • Vipin Kumar Singh

    (Department of Mathematics, Banaras Hindu University, Varanasi-221005, India)

Abstract

In this paper, we design a new third order Newton-like method and establish its convergence theory for finding the approximate solutions of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis of our third order Newton-like method under the ω -continuity condition. Then we apply our approach to solve nonlinear fixed point problems and Fredholm integral equations, where the first derivative of an involved operator does not necessarily satisfy the Hölder and Lipschitz continuity conditions. Several numerical examples are given, which compare the applicability of our convergence theory with the ones in the literature.

Suggested Citation

  • D. R. Sahu & Ravi P. Agarwal & Vipin Kumar Singh, 2018. "A Third Order Newton-Like Method and Its Applications," Mathematics, MDPI, vol. 7(1), pages 1-22, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2018:i:1:p:31-:d:194000
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/1/31/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/1/31/
    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:7:y:2018:i:1:p:31-:d:194000. 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.