On the Semi-Local Convergence of a Third Order Scheme for Solving Nonlinear Equations

Abstract

The semi-local convergence analysis of a third order scheme for solving nonlinear equation in Banach space has not been given under Lipschitz continuity or other conditions. Our goal is to extend the applicability of the Cordero-Torregrosa scheme in the semi-local convergence under conditions on the first Fréchet derivative of the operator involved. Majorizing sequences are used for proving our results. Numerical experiments testing the convergence criteria are given in this study.