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Sequentially lower complete spaces and Ekeland's variational principle.
- Source :
-
Acta Mathematica Sinica . Aug2015, Vol. 31 Issue 8, p1289-1302. 14p. - Publication Year :
- 2015
-
Abstract
- By using sequentially lower complete spaces (see [Zhu, J., Wei, L., Zhu, C. C.: Caristi type coincidence point theorem in topological spaces. J. Applied Math., 2013, ID 902692 (2013)]), we give a new version of vectorial Ekeland's variational principle. In the new version, the objective function is defined on a sequentially lower complete space and taking values in a quasi-ordered locally convex space, and the perturbation consists of a weakly countably compact set and a non-negative function p which only needs to satisfy p( x, y) = 0 iff x = y. Here, the function p need not satisfy the subadditivity. From the new Ekeland's principle, we deduce a vectorial Caristi's fixed point theorem and a vectorial Takahashi's non-convex minimization theorem. Moreover, we show that the above three theorems are equivalent to each other. By considering some particular cases, we obtain a number of corollaries, which include some interesting versions of fixed point theorem. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 31
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 103708204
- Full Text :
- https://doi.org/10.1007/s10114-015-4541-9