Convergence criteria of the generalized newton method and uniqueness of solution for generalized equations

Under a generalized L-average Lipschitz condition, we establish a convergence criterion around an initial point regarding the generalized Newton method for solving a generalized equation 0 ∈ F(x)+T(x), where F is Fréchet differentiable and T is set-valued and maximal monotone. Moreover, wc also get an estimation of uniqueness ball for a solution of the generalized equation. As applications, we obtain Kantorovich type theorem under the classical Lipschitz condition, convergence results under the γ-condition, and Smale's point estimate theory. Our results extend some corresponding results in [22].