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In this paper we consider a version of the Kantorovich's theorem for solvingthe generalized equation $F(x)+T(x)\ni 0$, where $F$ is a Fr\'echet derivativefunction and $T$ is a set-valued and maximal monotone acting between Hilbertspaces. We show that this method is quadratically convergent to a solution of$F(x)+T(x)\ni 0$. We have used the idea of majorant function, which relaxes theLipschitz continuity of the derivative $F'$. It allows us to obtain the optimalconvergence radius, uniqueness of solution and also to solving generalizedequations under Smale's condition.

On the Kantorovich's theorem for Newton's method for solving generalized equations under the majorant condition