On the semilocal convergence of a three steps Newton-type iterative process under mild convergence conditions

  1. Hernández-Verón, M.A. 1
  2. Martínez, E. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad Politécnica de Valencia
    info

    Universidad Politécnica de Valencia

    Valencia, España

    ROR https://ror.org/01460j859

Journal:
Numerical Algorithms

ISSN: 1017-1398

Year of publication: 2015

Volume: 70

Issue: 2

Pages: 377-392

Type: Article

DOI: 10.1007/S11075-014-9952-7 SCOPUS: 2-s2.0-84942503350 WoS: WOS:000361819600009 GOOGLE SCHOLAR

More publications in: Numerical Algorithms

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Abstract

In this paper the semilocal convergence for an alternative to the three steps Newton’s method with frozen derivative is presented. We analyze the generalization of convergence conditions given by w-conditioned non-decreasing functions instead of the first derivative Lipschitz or Holder continuous given by other authors. A nonlinear integral equation of mixed Hammerstein type is considered for illustrating the new theoretical results obtained in this paper, where previous results can not be satisfied.