Ekeland Variational Principle in asymmetric locally convex spaces

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• 作者：S. Cobza艧 ^{scobzas@math.ubbcluj.ro}
• 关键词：46A03 ; 46A19 ; 49N99 ; 54E15 ; 54E55 ; 58E30
• 刊名：Topology and its Applications
• 出版年：2012
• 期刊代码：60_01668641
• 类别：mt
• 出版时间：15 June-1 July, 2012
• 卷：159
• 期：10-11
• 页码：2558-2569
• 文件大小：209 K

摘要

In this paper we prove two versions of Ekeland Variational Principle in asymmetric locally convex spaces. The first one is based on a version of Ekeland Variational Principle in asymmetric normed spaces proved in S. Cobza艧, Topology Appl. 158 (8) (2011) 1073-1084. For the proof we need to study the completeness with respect to the asymmetric norm (the Minkowski functional) of the subspace of an asymmetric locally convex space X generated by a convex subset A of X (the analog of Banach disk). The second one is based on the existence of minimal elements (with respect to an appropriate order) in quasi-uniform spaces satisfying some completeness conditions, obtained as a consequence of Brezis-Browder maximality principle.