We present a convergence analysis for a damped Newton like method with modified right-hand side vector in order to approximate a locally unique solution of a nonlinear equation in a Banach spaces setting. In the special case when the method is defined on R-m, our method provides computable error estimates based on the initial data. Such estimates were not given in relevant studies such as. Numerical examples further validating the theoretical results are also presented in this study. (C) 2015 Elsevier Inc. All rights reserved.