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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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503205029 |
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| _version_ | 1832551345125588992 |
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| author | W. A. Kirk |
| author_facet | W. A. Kirk |
| author_sort | W. A. Kirk |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-0809f892d5b041358baf01d52edd71e3 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0809f892d5b041358baf01d52edd71e32025-02-03T06:01:42ZengWileyAbstract 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 |
| spellingShingle | W. A. Kirk Transfinite methods in metric fixed-point theory Abstract and Applied Analysis |
| title | 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_short | Transfinite methods in metric fixed-point theory |
| title_sort | transfinite methods in metric fixed point theory |
| url | http://dx.doi.org/10.1155/S1085337503205029 |
| work_keys_str_mv | AT wakirk transfinitemethodsinmetricfixedpointtheory |