On the Convergence of Perturbed Newton-like Methods in Banach Space and Applications

In this study we use disturbed Newton-like methods to approximate a locally unique solution of a nonlinear equation containing a nondiierentiable term. We choose the linear operators to be inverted at every step of the computation of the Newton iterates to be associated not only with the diierentiable part of the equation as it has happened so far but also with the nondiierentiable part. This way the upper error bounds on the distances are smaller than before.sovskii theorem, divided diierence of order one, Fr echet-derivative.