Weak compactness is not equivalent to the fixed point property in \(c\)

DOI10.1016/j.jmaa.2015.05.050zbMath1325.47099OpenAlexW593600692MaRDI QIDQ2352196

Torrey M. Gallagher, Chris Lennard, Roxana Popescu

Publication date: 30 June 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.05.050

zbMATH Keywords

nonexpansive mappingretractionfixed point propertyhyperconvex metric spacenon-weakly compact, closed, bounded, convex set

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Geometry and structure of normed linear spaces (46B20) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items (9)

A fixed-point characterization of weak compactness in Banach spaces with unconditional Schauder basis ⋮ The nonexpansive and mean nonexpansive fixed point properties are equivalent for affine mappings ⋮ Fixed points and common fixed points for orbit-nonexpansive mappings in metric spaces ⋮ Hölder-contractive mappings, nonlinear extension problem and fixed point free results ⋮ A fixed-point characterization of weakly compact sets in \(L_1(\mu)\) spaces ⋮ Weak compactness and fixed point property for affine bi-Lipschitz maps ⋮ A Large Class of Non-weakly Compact Subsets in a Renorming of $$c_0$$ with FPP ⋮ New examples of subsets of \(c\) with the FPP and stability of the FPP in hyperconvex spaces ⋮ Basis selection and fixed point results for affine mappings

Cites Work

• The fixed point property in \(c_0\) with an equivalent norm
• Extension of uniformly continuous transformations and hyperconvex metric spaces
• There is an equivalent norm on \(\ell_1\) that has the fixed point property
• Irregular convex sets with fixed-point property for nonexpansive mappings
• Existence of Fixed Points of Nonexpansive Mappings in Certain Banach Lattices
• Weak compactness is equivalent to the fixed point property in $c_0$
• Characterizations of weakly compact sets and new fixed point free maps in c₀
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