Expanding the applicability of secant-like methods for solving nonlinear equations

  1. Argyros, I.K. 2
  2. Ezquerro, J.A. 1
  3. Hernández-Verón, M.A. 1
  4. Hilout, S. 3
  5. Romero, N. 1
  6. Velasco, A.I. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Cameron University
    info

    Cameron University

    Lawton, Estados Unidos

    ROR https://ror.org/00rgv0036

  3. 3 University of Poitiers
    info

    University of Poitiers

    Poitiers, Francia

    ROR https://ror.org/04xhy8q59

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Journal:
Carpathian Journal of Mathematics

ISSN: 1584-2851

Year of publication: 2015

Volume: 31

Issue: 1

Pages: 11-30

Type: Article

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SCOPUS: 2-s2.0-84978968814 WoS: WOS:000351804500002 GOOGLE SCHOLAR

More publications in: Carpathian Journal of Mathematics

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Ecuaciones no lineales y métodos iterativos. Aplicaciones a problemas de optimización y ecuaciones matriciales. Nonlinear equations and iterative methods. Applications to optimization problems and matrix equations.

2015/00069/001

Abstract

We use the method of recurrent functions to provide a new semilocal convergence analysis for secant-like methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our sufficient convergence criteria are weaker than in earlier studies such as [18, 19, 20, 21, 25, 26]. Therefore, the new approach has a larger convergence domain and uses the same constants. A numerical example involving a nonlinear integral equation of mixed Hammerstein type is given to illustrate the advantages of the new approach. Another example of nonlinear integral equations is presented to show that the old convergence criteria are not satisfied but the new convergence are satisfied.