ON A LOCAL CHARACTERIZATION OF SOME NEWTON-LIKE METHODS OF R-ORDER AT LEAST THREE UNDER WEAK CONDITIONS IN BANACH SPACES

Title & Authors
ON A LOCAL CHARACTERIZATION OF SOME NEWTON-LIKE METHODS OF R-ORDER AT LEAST THREE UNDER WEAK CONDITIONS IN BANACH SPACES
Argyros, Ioannis K.; George, Santhosh;

Abstract
We present a local convergence analysis of some Newton-like methods of R-order at least three in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second $\small{Fr{\acute{e}}chet}$-derivative of the operator involved. These conditions are weaker that the corresponding ones given by Hernandez, Romero [10] and others [1], [4]-[9] requiring hypotheses up to the third $\small{Fr{\acute{e}}chet}$ derivative. Numerical examples are also provided in this study.
Keywords
Newton-like methods;R-order of convergence;Banach space;local convergence;$\small{Fr{\acute{e}}chet}$-derivative;
Language
English
Cited by
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