Dowling, P. N.; Lennard, C. J.; Turett, B. Characterizations of weakly compact sets and new fixed point free maps in \(c_0\). (English) Zbl 1037.47039 Stud. Math. 154, No. 3, 277-293 (2003). 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. Reviewer: Ioan A. Rus (Cluj-Napoca) Cited in 2 ReviewsCited in 11 Documents MSC: 47H10 Fixed-point theorems 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 46B50 Compactness in Banach (or normed) spaces Keywords:Banach space \(c_0\); weakly compact sets; fixed point free maps PDFBibTeX XMLCite \textit{P. N. Dowling} et al., Stud. Math. 154, No. 3, 277--293 (2003; Zbl 1037.47039) Full Text: DOI