We provide a new semilocal result for the quadratic convergence of Newton's method under ω*-conditioned second Fréchet derivative on a Banach space. This way we can handle equations where the usual Lipschitz-type conditions are not verifiable. An application involving nonlinear integral equations and two boundary value problems is provided. It turns out that a similar result using ω-conditioned hypotheses can provide usable error estimates indicating only linear convergence for Newton's method.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am38-3-5, author = {Ioannis K. Argyros and Sa\"\i d Hilout}, title = {On the convergence of Newton's method under $\omega$*-conditioned second derivative}, journal = {Applicationes Mathematicae}, volume = {38}, year = {2011}, pages = {341-355}, zbl = {1230.65063}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am38-3-5} }
Ioannis K. Argyros; Saïd Hilout. On the convergence of Newton's method under ω*-conditioned second derivative. Applicationes Mathematicae, Tome 38 (2011) pp. 341-355. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am38-3-5/