Approximate Benson efficient solutions for set-valued equilibrium problems

In locally convex Hausdorff topological vector spaces, the approximate Benson efficient solution is proposed for set-valued equilibrium problems and its relationship to the Benson efficient solution is discussed. Under the assumption of generalized convexity, by using a separation theorem for convex...

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Bibliographic Details
Published in:Journal of inequalities and applications 2020-04, Vol.2020 (1), p.1-16, Article 87
Main Authors: Hu, Shasha, Xu, Yihong, Niu, Zhichao
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Approximate Benson efficient solution
Convexity
Equilibrium
Mathematics
Mathematics and Statistics
Near cone-subconvexlikeness
Optimality condition
Set-valued equilibrium problem
Vector spaces
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Summary:In locally convex Hausdorff topological vector spaces, the approximate Benson efficient solution is proposed for set-valued equilibrium problems and its relationship to the Benson efficient solution is discussed. Under the assumption of generalized convexity, by using a separation theorem for convex sets, Kuhn–Tucker-type and Lagrange-type optimality conditions for set-valued equilibrium problems are established, respectively.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-020-02352-6