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The failure of the fixed point property for unbounded sets in $ c_0$


Author: T. Domínguez Benavides
Journal: Proc. Amer. Math. Soc. 140 (2012), 645-650
MSC (2010): Primary 47H09, 47H10; Secondary 46B20
DOI: https://doi.org/10.1090/S0002-9939-2011-10938-9
Published electronically: June 17, 2011
MathSciNet review: 2846334
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Abstract: In this paper we prove that for every unbounded convex closed set $ C$ in $ c_0$ there exists a nonexpansive mapping $ T:C\to C$ which is fixed point free. This result solves in a negative sense a question that has remained open for some time in Metric Fixed Point Theory.


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Additional Information

T. Domínguez Benavides
Affiliation: Facultad de Matemáticas, Universidad de Sevilla, P.O. Box 1160, 41080 Sevilla, Spain
Email: tomasd@us.es

DOI: https://doi.org/10.1090/S0002-9939-2011-10938-9
Received by editor(s): November 9, 2010
Received by editor(s) in revised form: December 3, 2010
Published electronically: June 17, 2011
Additional Notes: The author was partially supported by MCIN, Grant MTM 2009-10696-C02-01, and Andalusian Regional Government Grant FQM-127
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2011 American Mathematical Society

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