The failure of the fixed point property for unbounded sets in 𝑐₀

Benavides, T.

doi:10.1090/S0002-9939-2011-10938-9

The failure of the fixed point property for unbounded sets in

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 in 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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