On a connection between the fixed point property and \(L^{\infty}(\Omega,\Sigma,\mu)\)

DOI10.1016/J.NA.2006.02.029zbMath1121.46015OpenAlexW1497150193MaRDI QIDQ875279

Cleon S. Barroso

Publication date: 13 April 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.02.029

zbMATH Keywords

fixed point propertypointwise nonexpansive mapping\(L^\infty(\Omega,\Sigma, \mu)\)weakly compact convex set

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Fixed-point theorems (47H10) Geometry and structure of normed linear spaces (46B20) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items (1)

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Cites Work

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• Nonstandard methods in fixed point theory
• The fixed point property for subsets of some classical Banach spaces
• The Fixed Point Property for Non-Expansive Mappings, II
• Equivalent Norms and the Fixed Point Property for Nonexpansive Mappings
• A Fixed Point Free Nonexpansive Map
• The Fixed Point Property for Non-Expansive Mappings
• Existence of Fixed Points of Nonexpansive Mappings in Certain Banach Lattices
• On the behavior of weak convergence under nonlinearities and applications
• Reflexivity and approximate fixed points
• FIXED-POINT THEOREMS FOR NONCOMPACT MAPPINGS IN HILBERT SPACE
• NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE
• A Fixed Point Theorem for Mappings which do not Increase Distances
• Equivalent Norms for Sobolev Spaces
• The \(\tau\)-fixed point property for nonexpansive mappings

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