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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A fixed point free nonexpansive map


Author: Dale E. Alspach
Journal: Proc. Amer. Math. Soc. 82 (1981), 423-424
MSC: Primary 47H10; Secondary 54H25
MathSciNet review: 612733
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Abstract: In this note we give an example of a weakly compact convex subset of $ {L_1}[0,1]$ that fails to have the fixed point property for nonexpansive maps. This answers a long-standing question which was recently raised again by S. Reich [7].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0612733-0
PII: S 0002-9939(1981)0612733-0
Keywords: Fixed point theory
Article copyright: © Copyright 1981 American Mathematical Society