Fixed Point Theorems for Nonexpansive Mappings on Nonconvex Sets in Uced Banach Spaces
نویسندگان
چکیده
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 spaceX which is uniformly convex in every direction. Furthermore, if {Ti}i∈I is any compatible family of strongly nonexpansive self-mappings on such a C and the graphs of Ti, i∈ I, have a nonempty intersection, then Ti, i∈ I, have a common fixed point in C .
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