The Existence of Cone Critical Point and Common Fixed Point with Applications
We first establish some new critical point theorems for nonlinear dynamical systems in cone metric spaces or usual metric spaces, and then we present some applications to generalizations of Dancš-Hegedüs-Medvegyev's principle and the existence theorem related with Ekeland's variational pri...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/985797 |
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| _version_ | 1832554565604474880 |
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| author | Wei-Shih Du |
| author_facet | Wei-Shih Du |
| author_sort | Wei-Shih Du |
| collection | DOAJ |
| description | We first establish some new critical point theorems for nonlinear dynamical
systems in cone metric spaces or usual metric spaces, and then we present some applications
to generalizations of Dancš-Hegedüs-Medvegyev's principle and the existence theorem related with
Ekeland's variational principle, Caristi's common fixed point theorem for multivalued maps, Takahashi's
nonconvex minimization theorem, and common fuzzy fixed point theorem. We also obtain
some fixed point theorems for weakly contractive maps in the setting of cone metric spaces and focus
our research on the equivalence between scalar versions and vectorial versions of some results of fixed
point and others. |
| format | Article |
| id | doaj-art-544fc63fb50041749e183614428846a4 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-544fc63fb50041749e183614428846a42025-02-03T05:51:05ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/985797985797The Existence of Cone Critical Point and Common Fixed Point with ApplicationsWei-Shih Du0Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824, TaiwanWe first establish some new critical point theorems for nonlinear dynamical systems in cone metric spaces or usual metric spaces, and then we present some applications to generalizations of Dancš-Hegedüs-Medvegyev's principle and the existence theorem related with Ekeland's variational principle, Caristi's common fixed point theorem for multivalued maps, Takahashi's nonconvex minimization theorem, and common fuzzy fixed point theorem. We also obtain some fixed point theorems for weakly contractive maps in the setting of cone metric spaces and focus our research on the equivalence between scalar versions and vectorial versions of some results of fixed point and others.http://dx.doi.org/10.1155/2011/985797 |
| spellingShingle | Wei-Shih Du The Existence of Cone Critical Point and Common Fixed Point with Applications Journal of Applied Mathematics |
| title | The Existence of Cone Critical Point and Common Fixed Point with Applications |
| title_full | The Existence of Cone Critical Point and Common Fixed Point with Applications |
| title_fullStr | The Existence of Cone Critical Point and Common Fixed Point with Applications |
| title_full_unstemmed | The Existence of Cone Critical Point and Common Fixed Point with Applications |
| title_short | The Existence of Cone Critical Point and Common Fixed Point with Applications |
| title_sort | existence of cone critical point and common fixed point with applications |
| url | http://dx.doi.org/10.1155/2011/985797 |
| work_keys_str_mv | AT weishihdu theexistenceofconecriticalpointandcommonfixedpointwithapplications AT weishihdu existenceofconecriticalpointandcommonfixedpointwithapplications |