Fixed point theorems for nonexpansive mappingson nonconvex sets in UCED Banach spaces

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 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 .