Convergence of the Newton's Method for generalized equations under the majorant condition

In this paper we consider Newton's method for solving the generalized equation in Hilbert spaces of the type $F(x)+T(x)\ni 0$, where $F$ is a Fr\'echet differentiable function and $T$ is a set-valued and maximal monotone. We show that this method is local quadratically convergent to a solution. The analysis presented based on Banach Perturbation Lemma for generalized equation and the majorant condition relaxing Lipschitz continuity of the derivative $F'$, allow to obtain the optimal convergence radius, uniqueness of solution and also unify some result pertaining the Newton's method theory.