Argyros, I.K.George, S.2026-02-082019Understanding Banach Spaces, 2019, Vol., , p. 115-12497815361674509781536167467https://doi.org/10.1007/s13399-023-04079-yhttps://idr.nitk.ac.in/handle/123456789/33841We 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.Banach spaceFréchet- derivativeHigh convergence order methodLocal convergence