On the local convergence of a Newton–Kurchatov-type method for non-differentiable operators

摘要

By means of a nice idea, a Newton–Kurchatov type iterative process is constructed for solving nonlinear equations in Banach spaces. We analyze the local convergence of this iterative process. This study have an important and novel feature, since it is applicable to non-differentiable operators. So far, most of the local convergence results considered by other authors may apply only to differentiable operators due to the conditions that are required on the solution of the nonlinear equation.