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Uniformly nonsquare Banach spaces have the fixed point property for nonexpansive mappings

Eva M. Mazcuñán-navarroJesús Garcia-falsetEnrique Llorens-fuster

subject

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsUniformly nonsquare spacesApproximation propertyEberlein–Šmulian theoremBanach spaceNonexpansive mappingsUniformly convex spaceBanach manifoldFixed-point propertyNearly uniform smoothnessFixed pointsReflexive spaceLp spaceAnalysisMathematics

description

Abstract It is shown that if the modulus Γ X of nearly uniform smoothness of a reflexive Banach space satisfies Γ X ′ ( 0 ) 1 , then every bounded closed convex subset of X has the fixed point property for nonexpansive mappings. In particular, uniformly nonsquare Banach spaces have this property since they are properly included in this class of spaces. This answers a long-standing question in the theory.

yearjournalcountryeditionlanguage
2006-04-01Journal of Functional Analysis
10.1016/j.jfa.2005.09.002http://dx.doi.org/10.1016/j.jfa.2005.09.002