Fixed point theorems for nonexpansive mappings on nonconvex sets in UCED Banach spaces

Wei-Shih Du, Young-Ye Huang and Chi-Lin Yen

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 31, 1-7

Abstract:

It is shown that every asymptotically regular or λ -firmly nonexpansive mapping T : C → C has a fixed point whenever C is a finite union of nonempty weakly compact convex subsets of a Banach space X which is uniformly convex in every direction. Furthermore, if { T i } i ∈ I is any compatible family of strongly nonexpansive self-mappings on such a C and the graphs of T i , i ∈ I , have a nonempty intersection, then T i , i ∈ I , have a common fixed point in C .

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:146534

DOI: 10.1155/S0161171202107113

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