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Some renormings with the stable fixed point property


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Opened Access Some renormings with the stable fixed point property
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Author: Domínguez Benavides, Tomás
Phothi, Supaluk
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2013
Published in: Fixed Point Theory: An International Journal on Fixed Point Theory, Computation and Applications, 14 (1), 59-66.
Document type: Article
Abstract: In this paper, we prove that for any number λ < (√33−3)/2, any separable space X can be renormed in such a way that X satisfies the weak fixed point property for non-expansive mappings and this property is inherited for any other isomorphic space Y such that the Banach-Mazur distance between X and Y is less than λ. We also prove that any, in general nonseparable, Banach space with an extended unconditional basis can be renormed to satisfy the w-FPP with the same stability constant.
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