Transfinite methods in metric fixed-point theory

W. A. Kirk

Abstract and Applied Analysis, 2003, vol. 2003, 1-14

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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:734212

DOI: 10.1155/S1085337503205029

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