Fixed points of asymptotically regular nonexpansive mappings on nonconvex sets

Wieslawa Kaczor
2003 Abstract and Applied Analysis  
It is shown that ifXis a Banach space andCis a union of finitely many nonempty, pairwise disjoint, closed, and connected subsets{Ci:1≤i≤n }ofX, and eachCihas the fixed-point property (FPP) for asymptotically regular nonexpansive mappings, then any asymptotically regular nonexpansive self-mapping ofChas a fixed point. We also generalize the Goebel-Schöneberg theorem to some Banach spaces with Opial's property.
doi:10.1155/s1085337503205054 fatcat:ftnu4vcv45ccbjl6wgitmzyc5q