Faculty Publications

Permanent URI for this communityhttps://idr.nitk.ac.in/handle/123456789/18736

Publications by NITK Faculty

Browse

Author: search.filters.author.Argyros, M.Subject: search.filters.subject.Banach space

Search Results

Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    Extended kung–traub methods for solving equations with applications
    (MDPI, 2021) Regmi, S.; Argyros, I.K.; George, S.; Magreñán Ruiz, Á.A.; Argyros, M.
    Kung and Traub (1974) proposed an iterative method for solving equations defined on the real line. The convergence order four was shown using Taylor expansions, requiring the existence of the fifth derivative not in this method. However, these hypotheses limit the utilization of it to functions that are at least five times differentiable, although the methods may converge. As far as we know, no semi-local convergence has been given in this setting. Our goal is to extend the applicability of this method in both the local and semi-local convergence case and in the more general setting of Banach space valued operators. Moreover, we use our idea of recurrent functions and conditions only on the first derivative and divided difference, which appear in the method. This idea can be used to extend other high convergence multipoint and multistep methods. Numerical experiments testing the convergence criteria complement this study. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
  • No Thumbnail Available
    Item
    On the Influence of Center-Lipschitz Conditions in the Convergence Analysis of Multi-point Iterative Methods
    (International Publications, 2022) Argyros, I.K.; George, S.; Argyros, M.
    The aim of this article is to extend the local as well as the semi-local convergence analysis of multi-point iterative methods using center Lipschitz conditions in combination with our idea, of the restricted convergence region. It turns out that this way a finer convergence analysis for these methods is obtained than in earlier works and without additional hypotheses. Numerical examples favoring our technique over earlier ones completes this article. © 2022, International Publications. All rights reserved.