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Characterizations of weakly compact sets and new fixed point free maps in \(c_0\). (English) Zbl 1037.47039

The authors give the following characterization of weak compactness for closed, bounded, convex subsets \(C\) of the Banach space \(c_0\): such a \(C\) is weakly compact if and only if all of its closed, convex, nonempty subsets have the fixed point property for nonexpansive mappings.

MSC:

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
46B50 Compactness in Banach (or normed) spaces
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