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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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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: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
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. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 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: The Pure and Applied Mathematics

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