On Fixed Point Theory of Monotone Mappings with Respect to a Partial Order Introduced by a Vector Functional in Cone Metric Spaces
We presented some maximal and minimal fixed point theorems of set-valued monotone mappings with respect to a partial order introduced by a vector functional in cone metric spaces. In addition, we proved not only the existence of maximal and minimal fixed points but also the existence of the largest...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/349305 |
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| _version_ | 1849407439291547648 |
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| author | Zhilong Li Shujun Jiang |
| author_facet | Zhilong Li Shujun Jiang |
| author_sort | Zhilong Li |
| collection | DOAJ |
| description | We presented some maximal and minimal fixed point theorems of set-valued monotone mappings with respect to a partial order introduced by a vector functional in cone metric spaces. In addition, we proved not only the existence of maximal and minimal fixed points but also the existence of the largest and the least fixed points of single-valued increasing mappings. It is worth mentioning that the results on single-valued mappings in this paper are still new even in the case of metric spaces and hence they indeed improve the recent results. |
| format | Article |
| id | doaj-art-444cfe22afa44a2cac4f4638588bc38f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-444cfe22afa44a2cac4f4638588bc38f2025-08-20T03:36:03ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/349305349305On Fixed Point Theory of Monotone Mappings with Respect to a Partial Order Introduced by a Vector Functional in Cone Metric SpacesZhilong Li0Shujun Jiang1School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, ChinaDepartment of Mathematics, Jiangxi University of Finance and Economics, Nanchang 330013, ChinaWe presented some maximal and minimal fixed point theorems of set-valued monotone mappings with respect to a partial order introduced by a vector functional in cone metric spaces. In addition, we proved not only the existence of maximal and minimal fixed points but also the existence of the largest and the least fixed points of single-valued increasing mappings. It is worth mentioning that the results on single-valued mappings in this paper are still new even in the case of metric spaces and hence they indeed improve the recent results.http://dx.doi.org/10.1155/2013/349305 |
| spellingShingle | Zhilong Li Shujun Jiang On Fixed Point Theory of Monotone Mappings with Respect to a Partial Order Introduced by a Vector Functional in Cone Metric Spaces Abstract and Applied Analysis |
| title | On Fixed Point Theory of Monotone Mappings with Respect to a Partial Order Introduced by a Vector Functional in Cone Metric Spaces |
| title_full | On Fixed Point Theory of Monotone Mappings with Respect to a Partial Order Introduced by a Vector Functional in Cone Metric Spaces |
| title_fullStr | On Fixed Point Theory of Monotone Mappings with Respect to a Partial Order Introduced by a Vector Functional in Cone Metric Spaces |
| title_full_unstemmed | On Fixed Point Theory of Monotone Mappings with Respect to a Partial Order Introduced by a Vector Functional in Cone Metric Spaces |
| title_short | On Fixed Point Theory of Monotone Mappings with Respect to a Partial Order Introduced by a Vector Functional in Cone Metric Spaces |
| title_sort | on fixed point theory of monotone mappings with respect to a partial order introduced by a vector functional in cone metric spaces |
| url | http://dx.doi.org/10.1155/2013/349305 |
| work_keys_str_mv | AT zhilongli onfixedpointtheoryofmonotonemappingswithrespecttoapartialorderintroducedbyavectorfunctionalinconemetricspaces AT shujunjiang onfixedpointtheoryofmonotonemappingswithrespecttoapartialorderintroducedbyavectorfunctionalinconemetricspaces |