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Search: MSC category 47H09 ( Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc. )

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1. CMB 1998 (vol 41 pp. 413)

Llorens-Fuster, Enrique; Sims, Brailey
The fixed point property in $\lowercase{c_0}$
A closed convex subset of $c_0$ has the fixed point property ($\fpp$) if every nonexpansive self mapping of it has a fixed point. All nonempty weak compact convex subsets of $c_0$ are known to have the $\fpp$. We show that closed convex subsets with a nonempty interior and nonempty convex subsets which are compact in a topology slightly coarser than the weak topology may fail to have the $\fpp$.

Categories:47H09, 47H10

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