$\ddot{o}$lder continuity;Lipschitz continuity;semilocal convergence;Newton-Kantorovich hypothesis;differential equation;"/> ON THE "TERRA INCOGNITA" FOR THE NEWTON-KANTROVICH METHOD WITH APPLICATIONS | Korea Science
ON THE "TERRA INCOGNITA" FOR THE NEWTON-KANTROVICH METHOD WITH APPLICATIONS

Title & Authors
ON THE "TERRA INCOGNITA" FOR THE NEWTON-KANTROVICH METHOD WITH APPLICATIONS
Argyros, Ioannis Konstantinos; Cho, Yeol Je; George, Santhosh;

Abstract
In this paper, we use Newton's method to approximate a locally unique solution of an equation in Banach spaces and introduce recurrent functions to provide a weaker semilocal convergence analysis for Newton's method than before [1]-[13], in some interesting cases, provided that the Fr$\small{\acute{e}}$chet-derivative of the operator involved is p-H$\small{\ddot{o}}$lder continuous (p$\small{{\in}}$(0, 1]). Numerical examples involving two boundary value problems are also provided.
Keywords
Newton's method;Banach space;recurrent functions;H$\small{\ddot{o}}$lder continuity;Lipschitz continuity;semilocal convergence;Newton-Kantorovich hypothesis;differential equation;
Language
English
Cited by
1.
On iterative computation of fixed points and optimization, Fixed Point Theory and Applications, 2015, 2015, 1
2.
LOCAL CONVERGENCE FOR SOME THIRD-ORDER ITERATIVE METHODS UNDER WEAK CONDITIONS, Journal of the Korean Mathematical Society, 2016, 53, 4, 781
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