Extended convergence analysis of the Newton–Potra method under weak conditions

We study a nonlinear equation with a nondifferentiable part. The semi-local convergence of the Newton–Potra method is proved under weaker (than in earlier research) conditions on derivatives and divided differences of the first order. Weaker semi-local convergence criteria and tighter error estimations are obtained. Hence, the applicability of this method is extended too. These advantages are obtained under the same computational effort.