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- W194052374 abstract "In this paper, we present two semilocal convergence theorems for Newton-like approximations which improve and extend a fundamental result obtained by Yamamoto (15) in 1987. In the first part of this paper, we obtain an improvement of Yamamoto's result. In fact we consider the case in which the involved operators satisfy Lipschitz hypotheses and we prove a convergence result for Newton-like approximations under weaker assumptions. In the second part of this paper, we extend the previous result to the more general case studied recently by Argyros in (3) in which the involved operators satisfy generalized Holder hypotheses. We conclude with a comparison between our result and the result obtained by Argyros in (3) and we show that, even if the two theorems are not in general comparable, in some interesting cases it is more convenient to apply our theorem." @default.
- W194052374 created "2016-06-24" @default.
- W194052374 creator A5054884858 @default.
- W194052374 date "2004-01-01" @default.
- W194052374 modified "2023-09-26" @default.
- W194052374 title "CONVERGENCE THEOREMS FOR NEWTON-LIKE METHODS FOR OPERATORS WITH GENERALIZED H¨ OLDER DERIVATIVE" @default.
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