Common fixed point theorems for compatible self-maps of Hausdorff topological spaces
The concept of proper orbits of a map g is introduced and results of the following type are obtained. If a continuous self-map g of a Hausdorff topological space X has relatively compact proper orbits, then g has a fixed point. In fact, g has a common fixed point with every continuous self-map f of...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2005-10-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/FPTA.2005.355 |
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doaj-dddac715d3b946ef88f395cf7db361e12020-11-25T00:22:34ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122005-10-012005335536310.1155/FPTA.2005.355Common fixed point theorems for compatible self-maps of Hausdorff topological spacesGerald F. JungckThe concept of proper orbits of a map g is introduced and results of the following type are obtained. If a continuous self-map g of a Hausdorff topological space X has relatively compact proper orbits, then g has a fixed point. In fact, g has a common fixed point with every continuous self-map f of X which is nontrivially compatible with g. A collection of metric and semimetric space fixed point theorems follows as a consequence. Specifically, a theorem by Kirk regarding diminishing orbital diameters is generalized, and a fixed point theorem for maps with no recurrent points is proved.http://dx.doi.org/10.1155/FPTA.2005.355 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Gerald F. Jungck |
| spellingShingle |
Gerald F. Jungck Common fixed point theorems for compatible self-maps of Hausdorff topological spaces Fixed Point Theory and Applications |
| author_facet |
Gerald F. Jungck |
| author_sort |
Gerald F. Jungck |
| title |
Common fixed point theorems for compatible self-maps of Hausdorff topological spaces |
| title_short |
Common fixed point theorems for compatible self-maps of Hausdorff topological spaces |
| title_full |
Common fixed point theorems for compatible self-maps of Hausdorff topological spaces |
| title_fullStr |
Common fixed point theorems for compatible self-maps of Hausdorff topological spaces |
| title_full_unstemmed |
Common fixed point theorems for compatible self-maps of Hausdorff topological spaces |
| title_sort |
common fixed point theorems for compatible self-maps of hausdorff topological spaces |
| publisher |
SpringerOpen |
| series |
Fixed Point Theory and Applications |
| issn |
1687-1820 1687-1812 |
| publishDate |
2005-10-01 |
| description |
The concept of proper orbits of a map g is introduced and results of the following type are obtained. If a continuous self-map g of a Hausdorff topological space X has relatively compact proper orbits, then g has a fixed point. In fact, g has a common fixed point with every continuous self-map f of X which is nontrivially compatible with g. A collection of metric and semimetric space fixed point theorems follows as a consequence. Specifically, a theorem by Kirk regarding diminishing orbital diameters is generalized, and a fixed point theorem for maps with no recurrent points is proved. |
| url |
http://dx.doi.org/10.1155/FPTA.2005.355 |
| work_keys_str_mv |
AT geraldfjungck commonfixedpointtheoremsforcompatibleselfmapsofhausdorfftopologicalspaces |
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