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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


The fixed point property and unbounded sets in Hilbert space

Author: William O. Ray
Journal: Trans. Amer. Math. Soc. 258 (1980), 531-537
MSC: Primary 47H09; Secondary 47H10
MathSciNet review: 558189
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Abstract: It is shown that a closed convex subset K of a real Hilbert space H has the fixed point property for nonexpansive mappings if and only if K is bounded.

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Additional Information

PII: S 0002-9947(1980)0558189-1
Keywords: Fixed points, nonexpansive operators
Article copyright: © Copyright 1980 American Mathematical Society