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An improved local convergence analysis for Newton–Steffensen-type method

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Abstract

We provide a local convergence analysis for Newton–Steffensen-type algorithm for solving nonsmooth perturbed variational inclusions in Banach spaces. Under new center–conditions and the Aubin continuity property, we obtain the linear local convergence of Newton–Steffensen method. Our results compare favorably with related obtained in (Argyros and Hilout, 2007 submitted; Hilout in J. Math. Anal. Appl. 339:753–761, 2008).

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Authors and Affiliations

  1. Department of Mathematics Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

  2. Laboratoire de Mathématiques et Applications, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962, Futuroscope Chasseneuil Cedex, France

    Saïd Hilout

Authors
  1. Ioannis K. Argyros
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  2. Saïd Hilout
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Correspondence to Ioannis K. Argyros.

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Argyros, I.K., Hilout, S. An improved local convergence analysis for Newton–Steffensen-type method. J. Appl. Math. Comput. 32, 111–118 (2010). https://doi.org/10.1007/s12190-009-0236-7

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  • DOI: https://doi.org/10.1007/s12190-009-0236-7

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