Faculty Publications

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Publications by NITK Faculty

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Author: search.filters.author.Cho, Y.J.Subject: search.filters.subject.Banach space

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    On the "terra incognita" for the newton-kantrovich method with applications
    (2014) Argyros, I.K.; Cho, Y.J.; George, S.
    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 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.
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    Improved local convergence analysis for a three point method of convergence order 1.839…
    (Korean Mathematical Society kms@kms.or.kr, 2019) Argyros, I.K.; Cho, Y.J.; George, S.
    In this paper, we present a local convergence analysis of a three point method with convergence order 1.839… for approximating a locally unique solution of a nonlinear operator equation in setting of Banach spaces. Using weaker hypotheses than in earlier studies, we obtain: larger radius of convergence and more precise error estimates on the distances involved. Finally, numerical examples are used to show the advantages of the main results over earlier results. © 2019 Korean Mathematical Society.
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    Local Convergence of Inexact Newton-Like Method under Weak Lipschitz Conditions
    (Springer, 2020) Argyros, I.K.; Cho, Y.J.; George, S.; Xiao, Y.
    The paper develops the local convergence of Inexact Newton-Like Method (INLM) for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The obtained results compare favorably with earlier ones such as [7, 13, 14, 18, 19]. A numerical example is also provided. © 2020, Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences.