On the local convergence of Newton's method for solving generalized equations with monotone operator 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. Under a majorant condition on the nonlinear function which is associated to the generalized equation, the convergence of the method, the optimal convergence radius and results on the convergence rate are established.