Wyniki wyszukiwania - BazTech

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 1999

Znaleziono wyników: 1

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Picard iterates

Sortuj według:

Ogranicz wyniki do:

Convergence of Picard iterates of nonexpansive mappings

Kirk W., Sims B.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 2

147-155

Let X be a Banach space, C a closed subset of X, and T : C --> C a nonexpansive mapping. Conditions are given which assure that if the fixed point set F(T) of T has nonempty interior then the Picard iterates of the mapping T always converge to a point of F(T). If T is asymptotically regular, it suffices to assume that the closed subsets of X are densely proximinal and that nested spheres in X have compact interfaces. Such spaces include, among others, those which have Rolewicz's property ([beta]). If X has strictly convex norm the asymptotic regularity assumption can be dropped and the nested sphere property holds trivially. Consequently the result holds for all reflexive locally uniformly convex spaces.