A fixed-point characterization of weakly compact sets in \(L_1(\mu)\) spaces

DOI10.1016/j.jmaa.2020.124228zbMath1451.46020OpenAlexW3027511132MaRDI QIDQ2195157

Chris Lennard, Roxana Popescu, Japón Pineda, Maria A.

Publication date: 8 September 2020

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.2020.124228

zbMATH Keywords

weak compactnessaffine mappingsnonexpansive mappingsLebesgue spacesuniformly Lipschitzian mappings

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Classical Banach spaces in the general theory (46B25) Compactness in topological linear spaces; angelic spaces, etc. (46A50)

Related Items

Basis selection and fixed point results for affine mappings

Cites Work

• Compactness and the fixed point property in \(\ell_{1}\)
• The fixed point property for subsets of some classical Banach spaces
• Weak compactness and fixed point property for affine mappings.
• Existence of fixed points in a class of convex sets
• Weak compactness is not equivalent to the fixed point property in \(c\)
• A fixed-point characterization of weak compactness in Banach spaces with unconditional Schauder basis
• Reflexivity is equivalent to the perturbed fixed point property for cascading nonexpansive maps in Banach lattices
• The failure of the fixed point property for unbounded sets in 𝑐₀
• Convex Sets with the Lipschitz Fixed Point Property are Compact
• Nonexpansive maps in generalized Orlicz spaces
• Fixed Points of Nonexpansive Mappings in Banach Lattices
• Irregular convex sets with fixed-point property for nonexpansive mappings
• The Fixed Point Property and Unbounded Sets in Hilbert Space
• A Fixed Point Free Nonexpansive Map
• A new convexity property that implies a fixed point property for $L_{1}$
• Existence of Fixed Points of Nonexpansive Mappings in Certain Banach Lattices
• Weak compactness is equivalent to the fixed point property in $c_0$
• Komlós’ theorem and the fixed point property for affine mappings
• Characterizations of weakly compact sets and new fixed point free maps in c₀
• Some Topological Properties of Convex Sets
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