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: |
Hindawi Limited
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/985797 |
| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |