A Convergence analysis of three-step Newton-like method under weak conditions in Banach spaces

Abstract

In this paper, we present a local and semi-local convergence analysis for a three-step Newton-like method in order to approximate a solution of nonlinear equations in a Banach space. The convergence ball and error estimates are given for these methods. Also, we give some numerical examples for this study. Our results are generalizations of the analogous ones recently proved by Sahu et al. [3].