We provide a semilocal convergence analysis for Newton-type methods using our idea of recurrent functions in a Banach space setting. We use Zabrejko-Zinčenko conditions. In particular, we show that the convergence domains given before can be extended under the same computational cost. Numerical examples are also provided to show that we can solve equations in cases not covered before.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am38-2-5,
author = {Ioannis K. Argyros and Sa\"\i d Hilout},
title = {Convergence domains under Zabrejko-Zin\v cenko conditions using recurrent functions},
journal = {Applicationes Mathematicae},
volume = {38},
year = {2011},
pages = {193-209},
zbl = {1221.65130},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am38-2-5}
}
Ioannis K. Argyros; Saïd Hilout. Convergence domains under Zabrejko-Zinčenko conditions using recurrent functions. Applicationes Mathematicae, Tome 38 (2011) pp. 193-209. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am38-2-5/