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Unified local convergence for a certain family of methods in Banach space

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Abstract

We provide a local convergence analysis for a unified family of methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. These methods have fourth-order convergence, when specialized in the finite dimensional Euclidean space. In contrast to the earlier studies using hypotheses up to the fifth Fréchet-derivative, we only use hypotheses on the first Fréchet-derivative and Lipschitz constants. The applicability of these methods is expanded this way. Numerical examples are presented to show that we can solve equations in cases not possible with earlier approaches.

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Authors and Affiliations

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

    Ioannis K. Argyros

  2. University Institute of Engineering and Technology, Panjab University, Chandigarh, 160 014, India

    Munish Kansal

Authors
  1. Ioannis K. Argyros
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  2. Munish Kansal
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Correspondence to Munish Kansal.

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Argyros, I.K., Kansal, M. Unified local convergence for a certain family of methods in Banach space. SeMA 73, 325–334 (2016). https://doi.org/10.1007/s40324-016-0071-3

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  • DOI: https://doi.org/10.1007/s40324-016-0071-3

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