Abstract and Applied Analysis
Volume 2003 (2003), Issue 2, Pages 83-91
doi:10.1155/S1085337503205054
Fixed points of asymptotically regular nonexpansive mappings on
nonconvex sets
Instytut Matematyki, Uniwersytet M. Curie–Skłodowskiej (UMCS), Lublin 20-031, Poland
Received 30 November 2001
Copyright © 2003 Wiesława Kaczor. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
It is shown that if X is a Banach space and C is a union of
finitely many nonempty, pairwise disjoint, closed, and connected
subsets {Ci:1≤i≤n } of X, and each Ci has the fixed-point property (FPP) for asymptotically regular nonexpansive
mappings, then any asymptotically regular nonexpansive self-mapping of C has a fixed point. We also generalize the
Goebel-Schöneberg theorem to some Banach spaces with Opial's
property.