Convergence of the Newton-Type Method for Generalized Equations
Keywords:Set-valued mapping, Generalized equation, Local convergence, Pseudo-Lipschitz mapping, Newton-type method
Let X and Y be real or complex Banach spaces. Suppose that f: X->Y is a Frechet differentiable function and F: X => 2Yis a set-valued mapping with closed graph. In the present paper, we study the Newton-type method for solving generalized equation 0 ? f(x) + F(x). We prove the existence of the sequence generated by the Newton-type method and establish local convergence of the sequence generated by this method for generalized equation.
GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 27-40
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