Abstract
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.
Citation
W. A. Kirk. "Transfinite methods in metric fixed-point theory." Abstr. Appl. Anal. 2003 (5) 311 - 324, 10 March 2003. https://doi.org/10.1155/S1085337503205029
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