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Extended Newton-type method and its convergence analysis for nonsmooth generalized equations

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Abstract

Let X and Y be Banach spaces and \(\Omega \) be an open subset of X. Suppose that \(f:{\Omega \subseteq X}\rightarrow {Y}\) is a single-valued function which is nonsmooth and it has point based approximations on \(\Omega \) and \(F:X\rightrightarrows 2^Y\) is a set-valued mapping with closed graph. An extended Newton-type method is introduced in the present paper for solving the nonsmooth generalized equation \(0\in {f(x)+F(x)}\). Semilocal and local convergence of this method are analyzed based on the concept of point-based approximation.

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  1. Department of Mathematics, University of Rajshahi, Rajshahi, 6205, Bangladesh

    M. H. Rashid

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  1. M. H. Rashid
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Rashid, M.H. Extended Newton-type method and its convergence analysis for nonsmooth generalized equations. J. Fixed Point Theory Appl. 19, 1295–1313 (2017). https://doi.org/10.1007/s11784-017-0415-3

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