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Section B

On the convergence region of Newton's method under Hölder continuity conditions

Pages 317-326 | Received 18 Dec 2006, Accepted 24 Feb 2008, Published online: 12 Sep 2008

References

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  • Argyros , I. K. 2004 . A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space . J. Math. Anal. Appl. , 298 : 374 – 387 .
  • Argyros , I. K. 2005 . Concerning the “terra" incognica between convergence regions of two Newton methods . Non. Anal. , 62 : 179 – 194 .
  • Argyros , I. K. 2005 . Approximate Solution of Operator Equations with Applications , Hackenscak, NJ, , U.S.A : World Scientific Publ. Co .
  • Cianciaruso , F. and DePascale , E. 2003 . Newton–Kantorovich approximations when the derivative is Hölderian: old and new results . Numer. Funct. Anal. Optimiz. , 24 ( 7 and 8 ) : 713 – 723 .
  • Cianciaruso , F. and DePascale , E. 2006 . Estimates of majorizing sequences in the Newton–Kantorovich method . Numer. Funct. Anal. Optim. , 27 ( 5 and 6 ) : 529 – 538 .
  • Kantorovich , L. V. and Akilov , G. P. 1982 . Functional Analysis in Normed Spaces , Oxford : Pergamon Press .

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