On the convergence of modified Newton methods for solving equations containing a non-differentiable term

We provide a semilocal convergence analysis for certain modified Newton methods for solving equations containing a non-differentiable term. The sufficient convergence conditions of the corresponding Newton methods are often taken as the sufficient conditions for the modified Newton methods. That is why the latter methods are not usually treated separately from the former. However, here we show that weaker conditions, as well as a finer error analysis than before can be obtained for the convergence of modified Newton methods. Numerical examples are also provided.