Applications of an HIDS Theorem to the Existence of Fixed Point, Abstract Equilibria and Optimization Problems
By applying hybrid inclusion and disclusion systems (HIDS), we establish several vectorial variants of system of Ekeland's variational principle on topological vector spaces, some existence theorems of system of parametric vectorial quasi-equilibrium problem, and an existence theorem of system...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/247236 |
| Summary: | By applying hybrid inclusion and disclusion systems (HIDS), we establish several vectorial variants
of system of Ekeland's variational principle on topological vector spaces, some existence theorems of system of parametric vectorial quasi-equilibrium
problem, and an existence theorem of system of the Stampacchia-type vectorial equilibrium problem. As an application, a vectorial minimization theorem is
also given. Moreover, we discuss some equivalence relations between our vectorial variant of Ekeland's variational principle, common fixed point
theorem, and maximal element theorem. |
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| ISSN: | 1085-3375 1687-0409 |