0000000000115258

AUTHOR

Antonio Jiménez-melado

showing 4 related works from this author

Isomorphically expansive mappings in $l_2$

1997

Pure mathematicsApplied MathematicsGeneral MathematicsExpansiveMathematicsProceedings of the American Mathematical Society
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The Dunkl–Williams constant, convexity, smoothness and normal structure

2008

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.

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 TheoryAnalysisMathematicsJournal of Mathematical Analysis and Applications
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A Mönch type fixed point theorem under the interior condition

2009

Abstract In this paper we show that the well-known Monch fixed point theorem for non-self mappings remains valid if we replace the Leray–Schauder boundary condition by the interior condition. As a consequence, we obtain a partial generalization of Petryshyn's result for nonexpansive mappings.

Discrete mathematicsMathematics::Functional AnalysisGeneralizationApplied MathematicsInterior conditionMathematics::Analysis of PDEsBanach spaceFixed-point theoremType (model theory)Mönch fixed point theoremBanach spacesStrictly star-shaped setLeray–Schauder conditionBoundary value problemAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Stability of the Fixed Point Property for Nonexpansive Mappings

2001

In 1971 Zidler [Zi 71] showed that every separable Banach space (X, ‖·‖) admits an equivalent renorming, (X, ‖·‖0), which is uniformly convex in every direction (UCED), and consequently it has weak normal structure and so the weak fixed point property (WFPP) [D-J-S 71].

Pure mathematicsStructure (category theory)Regular polygonBanach spaceFixed-point propertyStability (probability)MathematicsSeparable space
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