Abstract
For a finite and positive measure space ( Ω , Σ , μ ) and any weakly compact convex subset of L ∞ ( Ω , Σ , μ ) a fixed point theorem for a class of nonexpansive self-mappings is proved. An analogous result is obtained for the space C ( Ω ) . Also, for a bounded domain with C 1 boundary Ω ⊂ R N , we construct a family of Banach spaces H p ( Ω ) , p > 1 , which are continuously embedded in L ∞ ( Ω ) and possess the fixed point property.
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