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On a nonsmooth version of Newton’s method using locally lipschitzian operators

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Abstract

In this study we are concerned with the problem of approximating a locally unique solution of an operator equation in Banach space using Newton’s method. The differentiability of the operator involved is not assumed. We provide a semilocal convergence analysis utilized to solve problems that were not covered before. Numerical examples are also provided to justify our approach.

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

    Ioannis K. Argyros

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  1. Ioannis K. Argyros
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Correspondence to Ioannis K. Argyros.

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Argyros, I.K. On a nonsmooth version of Newton’s method using locally lipschitzian operators. Rend. Circ. Mat. Palermo 56, 5–16 (2007). https://doi.org/10.1007/BF03031424

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  • DOI: https://doi.org/10.1007/BF03031424

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