Argyros, I.K.Cho, Y.J.George, S.Xiao, Y.2026-02-052020Acta Mathematica Scientia, 2020, 40, 1, pp. 199-2102529602https://doi.org/10.1007/s10473-020-0113-0https://idr.nitk.ac.in/handle/123456789/24200The paper develops the local convergence of Inexact Newton-Like Method (INLM) for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The obtained results compare favorably with earlier ones such as [7, 13, 14, 18, 19]. A numerical example is also provided. © 2020, Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences.Banach spaceinexact Newton methodKantorovich hypothesesrecurrent functionssemilocal convergenceweak and center-weak Lipschitz condition