Near-infinity concentrated norms and the fixed point property for nonexpansive maps on closed, bounded, convex sets

DOI10.1016/j.jfa.2018.04.007zbMath1400.46009OpenAlexW2804177713WikidataQ129795445 ScholiaQ129795445MaRDI QIDQ1753335

C. J. Lennard, Barry Turett, Francisco Eduardo Castillo Santos, Helga Fetter Nathansky, Patrick N. Dowling, Japón Pineda, Maria A., Brailey Sims

Publication date: 29 May 2018

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://idus.us.es/handle//11441/80137

zbMATH Keywords

fixed point propertynonexpansive mappingsrenorming theory

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Isomorphic theory (including renorming) of Banach spaces (46B03) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

Related Items (5)

Fixed point properties and reflexivity in variable Lebesgue spaces ⋮ The fixed point property for nonexpansive type mappings in nonreflexive Banach spaces ⋮ Dual fixed point property on spaces of continuous functions under equivalent norms ⋮ Fixed point property of Hilbert modules over finite dimensional \(\mathrm{C}^*\)-algebras ⋮ Existence of fixed points in a class of convex sets

Cites Work

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• Renorming of \(\ell _{1}\) and the fixed point property
• There is an equivalent norm on \(\ell_1\) that has the fixed point property
• Every nonreflexive subspace of $L_1[0,1$ fails the fixed point property]
• The optimality of James’s distortion theorems

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