Prépublication AOC numéro 02-06

A Superquadratic Method for Solving Generalized Equations in the Holder Case
GEOFFROY, Michel - Laboratoire A.O.C., Université des Antilles et de la Guyane, Pointe-à-Pitre, F-97159 cedex
PIETRUS, Alain - Laboratoire A.O.C., Université des Antilles et de la Guyane, Pointe-à-Pitre, F-97159 cedex

We investigate the existence of some sequence (x_k) converging to a solution x^* of the generalized equation 0\in f(x)+G(x); where f is a function and G is a set-valued map acting in Banach spaces. We show that the previous sequence is locally superquadratic convergent to x^* whenever the second Fréchet derivative of the function f satisfies a Holder-type condition and some set-valued map involving G and f is M-pseudo-Lipschitz around (0,x^*).