Argyros, I.K.George, S.Senapati, K.2026-02-042024Journal of Analysis, 2024, 32, 2, pp. 697-7099713611https://doi.org/10.1007/s41478-023-00652-whttps://idr.nitk.ac.in/handle/123456789/21219In this study, we have extended the applicability of two-step methods with non-differentiable parts for solving nonlinear equations defined in Banach spaces. The convergence analysis uses conditions weaker than the ones in earlier studies. Other advantages include computable a priori error distances based on generalized conditions, an extended region of convergence as well as a better knowledge of the isolation for the solutions. By setting the divided differences equal to zero the results can be used to solve equations with differentiable part too. © The Author(s), under exclusive licence to The Forum D’Analystes 2023.47H1749M1565G99Banach spaceConvergenceIterative methodNon-differentiable operator