Extended convergence for two-step methods with non-differentiable parts in Banach spaces

In 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.