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- Title
An equilibrium version of set-valued Ekeland variational principle and its applications to set-valued vector equilibrium problems.
- Authors
Qiu, Jing
- Abstract
By using Gerstewitz functions, we establish a new equilibrium version of Ekeland variational principle, which improves the related results by weakening both the lower boundedness and the lower semi-continuity of the objective bimaps. Applying the new version of Ekeland principle, we obtain some existence theorems on solutions for set-valued vector equilibrium problems, where the most used assumption on compactness of domains is weakened. In the setting of complete metric spaces ( Z, d), we present an existence result of solutions for set-valued vector equilibrium problems, which only requires that the domain X ⊂ Z is countably compact in any Hausdorff topology weaker than that induced by d. When ( Z, d) is a Féchet space (i.e., a complete metrizable locally convex space), our existence result only requires that the domain X ⊂ Z is weakly compact. Furthermore, in the setting of non-compact domains, we deduce several existence theorems on solutions for set-valued vector equilibrium problems, which extend and improve the related known results.
- Subjects
VARIATIONAL principles; SET-valued maps; METRIC spaces; HAUSDORFF measures; VECTOR topology
- Publication
Acta Mathematica Sinica, 2017, Vol 33, Issue 2, p210
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-016-6184-x