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On Ha's version of set-valued Ekeland's variational principle.
- Source :
-
Acta Mathematica Sinica . Apr2012, Vol. 28 Issue 4, p717-726. 10p. - Publication Year :
- 2012
-
Abstract
- By using the concept of cone extensions and Dancs-Hegedus-Medvegyev theorem, Ha [Some variants of the Ekeland variational principle for a set-valued map. J. Optim. Theory Appl., 124, 187-206 (2005)] established a new version of Ekeland's variational principle for set-valued maps, which is expressed by the existence of strict approximate minimizer for a set-valued optimization problem. In this paper, we give an improvement of Ha's version of set-valued Ekeland's variational principle. Our proof is direct and it need not use Dancs-Hegedus-Medvegyev theorem. From the improved Ha's version, we deduce a Caristi-Kirk's fixed point theorem and a Takahashi's nonconvex minimization theorem for set-valued maps. Moreover, we prove that the above three theorems are equivalent to each other. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 28
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 72899988
- Full Text :
- https://doi.org/10.1007/s10114-011-0294-2