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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.15 No.2

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ON THE CONVERGENCE OF NEWTON'S METHOD ANDLOCALLY H？OLDERIAN OPERATORS

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2008, v.15 no.2, pp.111-120
Argyros, Ioannis K.
Argyros,, I. K. (2008). ON THE CONVERGENCE OF NEWTON'S METHOD ANDLOCALLY H？OLDERIAN OPERATORS. , 15(2), 111-120.

Abstract

A semi local convergence analysis is provided for Newton's method in a Banach space setting. The operators involved are only locally Holderian. We make use of a point-based approximation and center-Holderian hypotheses. This approach can be used to approximate solutions of equations involving nonsmooth operators.

keywords
Newton's method, Banach space, locally <tex> $H{\ddot{o}}lderian$</tex> operators, point-based approximation, semilocal convergence, successive substitutions, fixed point

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

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