An equilibrium version of set-valued Ekeland variational principle and its applications to set-valued vector equilibrium problems

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• 作者：Jing Hui Qiu
• 关键词：Ekeland variational principle ; set ; valued vector equilibrium problem ; quasi ; ordered locally convex space ; lower semi ; continuity ; lower boundedness
• 刊名：Acta Mathematica Sinica, English Series
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：33
• 期：2
• 页码：210-234
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1439-7617
• 卷排序：33

文摘

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.