Argyros, I.K.George, S.2026-02-052020Creative Mathematics and Informatics, 2020, 29, 2, pp. 113-1201584286Xhttps://doi.org/10.37193/CMI.2020.02.01https://idr.nitk.ac.in/handle/123456789/23714We present a local convergence analysis for inexact Newton methods 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. Numerical examples are also provided in this study. © 2020, SINUS Association. All rights reserved.Banach spaceFréchet-derivativeHigh convergence order methodLocal Convergence