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

 

On weak compactness
and countable weak compactness
in fixed point theory


Authors: John Kulesza and Teck-Cheong Lim
Journal: Proc. Amer. Math. Soc. 124 (1996), 3345-3349
MSC (1991): Primary 47H10, 47H09; Secondary 54E50, 54D30
MathSciNet review: 1328357
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Abstract: We prove that weak compactness and countable weak compactness in metric spaces are not equivalent. However, if the metric space has normal structure, they are equivalent. It follows that some fixed point theorems proved recently are consequences of a classical theorem of Kirk.


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Additional Information

John Kulesza
Affiliation: Department of Mathematics, George Mason University, 4400 University Drive, Fairfax, Virginia 22030
Email: jkulesza@gmu.edu

Teck-Cheong Lim
Affiliation: Department of Mathematics, George Mason University, 4400 University Drive, Fairfax, Virginia 22030
Email: tlim@gmu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03390-4
PII: S 0002-9939(96)03390-4
Keywords: Nonexpansive mappings, fixed point, normal structure, weak compact, countable weak compact, uniform normal structure
Received by editor(s): January 3, 1995
Received by editor(s) in revised form: March 27, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society