Prépublication AOC numéro 02-04

Acceleration of Convergence in Dontchev's Iterative Method for Solving Variational Inclusions
GEOFFROY, Michel - Laboratoire A.O.C., Université des Antilles et de la Guyane, Pointe-à-Pitre, F-97157 cedex
HILOUT, Saïd - Département de Mathématiques Appliquées, Faculté des Sciences et Techniques, BP 523, Beni-Mellal, Maroc
PIETRUS, Alain - Laboratoire A.O.C., Université des Antilles et de la Guyane, Pointe-à-Pitre, F-97157 cedex



Mots Clés : Multiapplications, Aubin Continuity, Cubic Convergence.

Classification MSC : 47H04; 65K10
Abstract :
We investigate the existence of some sequence (xk) satisfying 0 Î f(xk)+ Ñf(xk) (xk+1-xk) + 1/2 Ñ 2 f(xk) (xk+1-xk)2 +G(xk+1) and converging to a solution x* of the generalized equation 0 Î 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 cubic convergent to x* whenever some set-valued map involving G, f and its first and second Fréchet derivatives is M-pseudo-Lipschitz around (0,x*).
Article : Postscript compressé Contact : michel.geoffroy@univ-ag.fr