Argyros, I.K.George, S.2026-02-052020Panamerican Mathematical Journal, 2020, 30, 3, pp. 13-2010649735https://idr.nitk.ac.in/handle/123456789/23827We introduce tangential-like conditions which in general are weaker than the usual Lipschitz-like conditions in order to show the local as well as the semi-local convergence of some iterative methods approximating solutions of nonlinear equations in Banach space. Numerical examples further validate the theoretical results showing that equations can be solved with the new conditions but not with the old ones. © 2020, International Publications. All rights reserved.Banach spaceHilbert spaceIll-posed problemsLoca/semi-local convergenceTangential-like conditions