Recherches et rapports sur les mathématiques

Extending the Applicability of an Ulm-Newton-like Method under Generalized Conditions in Banach Space

Ioannis K. Argyros and Santhosh George

The aim of this paper is to extend the applicability of an Ulm-Newtonlike method for approximating a solution of a nonlinear equation in a Ba-nach space setting. The su cient local convergence conditions are weaker than in earlier works leading to a larger radius of convergence and more precise error estimates on the distances involved. Numerical examples are also provided in this study. AMS Subject Classi cation: 65H10, 65G99, 65J15,49M15.