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The Dunkl–Williams constant, convexity, smoothness and normal structure

Antonio Jiménez-meladoEnrique Llorens-fusterEva M. Mazcuñán-navarro

subject

Smoothness (probability theory)Applied MathematicsMathematical analysisStructure (category theory)Banach spaceMathematics::Classical Analysis and ODEsCharacterization (mathematics)Fixed-point propertyJames constantSmoothnessNormal structureConvexityPhysics::History of PhysicsDunkl–Williams constantConvexityMathematics::Quantum AlgebraConstant (mathematics)Mathematics::Representation TheoryAnalysisMathematics

description

Abstract In this paper we exhibit some connections between the Dunkl–Williams constant and some other well-known constants and notions. We establish bounds for the Dunkl–Williams constant that explain and quantify a characterization of uniformly nonsquare Banach spaces in terms of the Dunkl–Williams constant given by M. Baronti and P.L. Papini. We also study the relationship between Dunkl–Williams constant, the fixed point property for nonexpansive mappings and normal structure.

yearjournalcountryeditionlanguage
2008-06-01Journal of Mathematical Analysis and Applications
10.1016/j.jmaa.2007.11.045http://dx.doi.org/10.1016/j.jmaa.2007.11.045