The failure of the fixed point property for unbounded sets in $c_0$
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- by T. Domínguez Benavides
- Proc. Amer. Math. Soc. 140 (2012), 645-650
- DOI: https://doi.org/10.1090/S0002-9939-2011-10938-9
- Published electronically: June 17, 2011
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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.References
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Bibliographic Information
- T. Domínguez Benavides
- Affiliation: Facultad de Matemáticas, Universidad de Sevilla, P.O. Box 1160, 41080 Sevilla, Spain
- Email: tomasd@us.es
- 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
- © Copyright 2011 American Mathematical Society
- 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
- MathSciNet review: 2846334