Fixed points of asymptotically regular nonexpansive mappings on nonconvex sets
Kaczor, Wiesława
Abstr. Appl. Anal., Tome 2003 (2003) no. 7, p. 83-91 / Harvested from Project Euclid
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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 $\{C_i: 1\leq i\leq n\}$ of $X$ , and each $C_i$ 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.
Publié le : 2003-01-30
Classification:  47H10,  47H09,  47H20 
@article{1050426053,
     author = {Kaczor, Wies\l awa},
     title = {Fixed points of asymptotically regular nonexpansive mappings on
nonconvex sets},
     journal = {Abstr. Appl. Anal.},
     volume = {2003},
     number = {7},
     year = {2003},
     pages = { 83-91},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1050426053}
}

Kaczor, Wiesława. Fixed points of asymptotically regular nonexpansive mappings on
nonconvex sets. Abstr. Appl. Anal., Tome 2003 (2003) no. 7, pp.  83-91. http://gdmltest.u-ga.fr/item/1050426053/