Fixed points of asymptotically regular nonexpansive mappings onnonconvex sets
Wieslawa J Kaczor · Abstract and Applied Analysis · 2003
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.