Estimates of the radius of convergence of Newton's methods for variational inclusions in Banach spaces are investigated under a weak Lipschitz condition on the first Fréchet derivative. We establish the linear convergence of Newton's and of a variant of Newton methods using the concepts of pseudo-Lipschitz set-valued map and ω-conditioned Fréchet derivative or the center-Lipschitz condition introduced by the first author.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am34-3-6,
author = {Ioannis K. Argyros and Sa\"\i d Hilout},
title = {Newton's methods for variational inclusions under conditioned Fr\'echet derivative},
journal = {Applicationes Mathematicae},
volume = {34},
year = {2007},
pages = {349-357},
zbl = {1135.47051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-3-6}
}
Ioannis K. Argyros; Saïd Hilout. Newton's methods for variational inclusions under conditioned Fréchet derivative. Applicationes Mathematicae, Tome 34 (2007) pp. 349-357. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-3-6/