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 | References | Similar Articles | Additional Information
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
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
