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ON THE SEMILOCAL CONVERGENCE OF A NEWTON-TYPE METHOD OF ORDER THREE  

Argyros, Ioannis K. (CAMERON UNIVERSITY, DEPARTMENT OF MATHEMATICS SCIENCES)
Hilout, Said (POITIERS UNIVERSITY, LABORATORIE DE MATHEMATIQUES ET APPLICATIONS)
Publication Information
The Pure and Applied Mathematics / v.17, no.1, 2010 , pp. 1-27 More about this Journal
Abstract
Wu and Zhao [17] provided a semilocal convergence analysis for a Newton-type method on a Banach space setting following the ideas of Frontini and Sormani [9]-[11]. In this study first: we point out inconsistencies between the hypotheses of Theorem 1 and the two examples given in [17], and then, we provide the proof in affine invariant form for this result. Then, we also establish new convergence results with the following advantages over the ones in [17]: weaker hypotheses, and finer error estimates on the distances involved. A numerical example is also provided to show that our results apply in cases other fail [17].
Keywords
Newton-type methods; Banach space; majorizing sequence; Fr$\acute{e}$chet-derivatives; semilocal convergence;
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