On the "terra incognita" for the newton-kantrovich method with applications

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dc.contributor.authorArgyros, I.K.
dc.contributor.authorCho, Y.J.
dc.contributor.authorGeorge, S.
dc.date.accessioned2026-02-05T09:34:16Z
dc.date.issued2014
dc.description.abstractIn 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 Fréchet-derivative of the operator involved is p-Hölder continuous (p ?(0, 1]). Numerical examples involving two boundary value problems are also provided. © 2014 Korean Mathematical Society.
dc.identifier.citationJournal of the Korean Mathematical Society, 2014, 51, 2, pp. 251-266
dc.identifier.issn3049914
dc.identifier.urihttps://doi.org/10.4134/JKMS.2014.51.2.251
dc.identifier.urihttps://idr.nitk.ac.in/handle/123456789/26516
dc.subjectBanach space
dc.subjectDifferential equation
dc.subjectHölder continuity
dc.subjectLipschitz continuity
dc.subjectNewton's method
dc.subjectNewton-kantorovich hypothesis
dc.subjectRecurrent functions
dc.subjectSemilocal convergence
dc.titleOn the "terra incognita" for the newton-kantrovich method with applications

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