Chebyshev-Secant-type Methods for Non-differentiable Operators

  1. Argyros, I.K. 2
  2. Ezquerro, J.A. 1
  3. Gutiérrez, J.M. 1
  4. Hernández, M.A. 1
  5. Hilout, S. 3
  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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Revista:
Milan Journal of Mathematics

ISSN: 1424-9286

Any de publicació: 2013

Volum: 81

Número: 1

Pàgines: 25-35

Tipus: Article

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DOI: 10.1007/S00032-012-0189-4 SCOPUS: 2-s2.0-84876945659 WoS: WOS:000318284400002 GOOGLE SCHOLAR

Altres publicacions en: Milan Journal of Mathematics

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Resum

In this paper we give a semilocal convergence theorem for a family of iterative methods for solving nonlinear equations defined between two Banach spaces. This family is obtained as a combination of the well known Secant method and Chebyshev method. We give a very general convergence result that allow the application of these methods to non-differentiable problems. © 2012 Springer Basel.