On the convergence of inexact two-point Newton-like methods on Banach spaces

Abstract

We present a unified convergence analysis of Inexact Newton-like methods in order to approximate a locally unique solution of a nonlinear operator equation containing a nondifferentiable term in a Banach space setting. The convergence conditions are more general and the error analysis more precise than in earlier studies such as (Argyros, 2007; Cătinaş, 2005; Cătinaş, 1994; Chen and Yamamoto, 1989; Dennis, 1968; Hernández and Romero, 2005; Potra and Pták, 1984; Rheinboldt, 1977). Special cases of our results can be used to find zeros of derivatives. Numerical examples are also provided in this study.