We present a unified convergence analysis of Inexact Newton like methods in order to approximate a locally unique solution of a nonlinear operator equation containing a nondifferentiable term in a Banach space setting. The convergence conditions are more general and the error analysis more precise than in earlier studies such as (Argyros, 2007: Catinas, 2005; Catinas, 1994; Chen and Yamamoto, 1989: Dennis, 1968: Hernandez and Romero, 2005; Potra and Ptak, 1984; Rheinboldt, 1977). Special cases of our results can be used to find zeros of derivatives. Numerical examples are also provided in this study. (C) 2015 Elsevier Inc. All rights reserved.