Argyros I.K.George S.2021-05-052021-05-052019Understanding Banach Spaces , Vol. , , p. 115 - 124https://idr.nitk.ac.in/handle/123456789/14621We present a local convergence analysis for a fifth-order method in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative of the operator involved. Earlier studies use hypotheses up to the fourth Fréchet-derivative [1]. Hence, the applicability of these methods is expanded under weaker hypotheses and less computational cost for the constants involved in the convergence analysis. Numerical examples are also provided in this study. © 2020 by Nova Science Publishers, Inc. All rights reserved.Book Chapter