数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (5): 1670-1676.doi: 10.1016/S0252-9602(14)60113-2
• 论文 • 上一篇
丘京辉
QIU Jing-Hui
摘要:
Let (E, ξ) = ind(En, ξn) be an inductive limit of a sequence (En, ξn)n∈N of locally convex spaces and let every step (En, ξn) be endowed with a partial order by a pointed convex (solid) cone Sn. In the framework of inductive limits of partially ordered locally convex spaces, the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence (Sn)n∈N of ordering cones is non-conflicting, an existence theorem on lastingly weakly efficient points is presented. From this, an existence theorem on lastingly globally properly efficient points is deduced.
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