Wei-Shih Du, Young-Ye Huang, Chi-Lin Yen, "Fixed point theorems for nonexpansive mappings on nonconvex sets in UCED Banach spaces", International Journal of Mathematics and Mathematical Sciences, vol. 31, Article ID 146534, 7 pages, 2002. https://doi.org/10.1155/S0161171202107113
Fixed point theorems for nonexpansive mappings on nonconvex sets in UCED Banach spaces
It is shown that every asymptotically regular or -firmly nonexpansive mapping has a fixed point whenever is a finite union of nonempty weakly compact convex subsets of a Banach space which is uniformly convex in every direction. Furthermore, if is any compatible family of strongly nonexpansive self-mappings on such a and the graphs of , , have a nonempty intersection, then , , have a common fixed point in .
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