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10 March 2003 Transfinite methods in metric fixed-point theory
W. A. Kirk
Abstr. Appl. Anal. 2003(5): 311-324 (10 March 2003). DOI: 10.1155/S1085337503205029


This is a brief survey of the use of transfinite induction in metric fixed-point theory. Among the results discussed in some detail is the author's 1989 result on directionally nonexpansive mappings (which is somewhat sharpened), a result of Kulesza and Lim giving conditions when countable compactness implies compactness, a recent inwardness result for contractions due to Lim, and a recent extension of Caristi's theorem due to Saliga and the author. In each instance, transfinite methods seem necessary.


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W. A. Kirk. "Transfinite methods in metric fixed-point theory." Abstr. Appl. Anal. 2003 (5) 311 - 324, 10 March 2003.


Published: 10 March 2003
First available in Project Euclid: 15 April 2003

zbMATH: 1022.54027
MathSciNet: MR1981268
Digital Object Identifier: 10.1155/S1085337503205029

Primary: 54H10 , 74H10

Rights: Copyright © 2003 Hindawi

Vol.2003 • No. 5 • 10 March 2003
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