Transfinite methods in metric fixed-point theory

Transfinite methods in metric fixed-point theory

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 comp...

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Main Author: W. A. Kirk
Format: Article
Language:English
Published: Hindawi Limited 2003-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/S1085337503205029
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spelling doaj-0809f892d5b041358baf01d52edd71e32020-11-24T22:32:51ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092003-01-012003531132410.1155/S1085337503205029Transfinite methods in metric fixed-point theoryW. A. Kirk0Department of Mathematics, The University of Iowa, Iowa City 52242-1419, IA, USAThis 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.http://dx.doi.org/10.1155/S1085337503205029
collection DOAJ
language English
format Article
sources DOAJ
author W. A. Kirk
spellingShingle W. A. Kirk
Transfinite methods in metric fixed-point theory
Abstract and Applied Analysis
author_facet W. A. Kirk
author_sort W. A. Kirk
title Transfinite methods in metric fixed-point theory
title_short Transfinite methods in metric fixed-point theory
title_full Transfinite methods in metric fixed-point theory
title_fullStr Transfinite methods in metric fixed-point theory
title_full_unstemmed Transfinite methods in metric fixed-point theory
title_sort transfinite methods in metric fixed-point theory
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2003-01-01
description 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.
url http://dx.doi.org/10.1155/S1085337503205029
work_keys_str_mv AT wakirk transfinitemethodsinmetricfixedpointtheory
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