Abstract
In this paper we introduce a monotone Newton-like method for the computations of fixed points of a class of nonlinear operators in ordered Banach spaces. We use a Lakshmikantham’s fixed point theorem [4, Theorem 1.2] and the classical Banach fixed point theorem to prove the convergence of this method. We prove also that under a suitable condition, the rate of convergence of the proposed method is superlinear. As an application we consider a class of nonlinear matrix equations.
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Mouhadjer, L., Benahmed, B. (2015). A Monotone Newton-Like Method for the Computation of Fixed Points. In: Le Thi, H., Pham Dinh, T., Nguyen, N. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. Advances in Intelligent Systems and Computing, vol 359. Springer, Cham. https://doi.org/10.1007/978-3-319-18161-5_29
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DOI: https://doi.org/10.1007/978-3-319-18161-5_29
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18160-8
Online ISBN: 978-3-319-18161-5
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