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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
DOI: https://doi.org/10.1090/S0002-9947-1980-0558189-1
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

DOI: https://doi.org/10.1090/S0002-9947-1980-0558189-1
Keywords: Fixed points, nonexpansive operators
Article copyright: © Copyright 1980 American Mathematical Society