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Let  X  and  Y  be Banach spaces. Letbe a Fréchet differentiable function andbe a set-valued mapping with closed graph. In this paper, a restricted Newton-type method has been introduced for solving the generalized equations of the form. Under some suitable conditions, we will establish the convergence criteria of the restricted Newton-type method, which ensures the existence and the convergence of any sequence generated by this method. More precisely, when the Fréchet derivative of  f  is continuous and Lipschitz continuous as well asis metrically regular, we analyze the semilocal and local convergence of the restricted Newton-type method. In addition, an example is given to show the reason for considering the metrically regular property instead of Lipschitz-like property of set-valued mapping in this paper.

Convergence properties of a restricted Newton-type method for generalized equations with metrically regular mappings