Weak convergence and nonlinear ergodic theorems for reversible semigroups of nonexpansive mappings.

Soit S un semi-groupe semi-topologique. Soit C un sous-ensemble convexe ferme d'un espace de Banach uniformement convexe E avec une norme differentiable de Frechet et S={T a ;a∈S} une representation continue de S comme des applications non-dilatation de C dans C telles que l'ensemble point fixe commun F(S) de S dans C est non vide. On demontre que si S est reversible a droite, alors pour tout x∈C, l'ensemble convexe ferme W(x)=∩F(φ) est constitue d'au lus un point ou W(x)∩{K S (x);s∈S},K S (x) est l'enveloppe convexe fermee de {T t x;t≥S} et t≥S signifie t=s ou t∈Ss

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