有界线性空间中的Phelps引理

摘要

将Phelps引理推广到有界线性空间.一个直接的应用是获得了Wong推广到有界线性空间中的Ekeland变分原理.而且Ng和郑在拓扑线性空间中的有效点存在性定理也容易得到.同时,给出了一个局部凸空间中的Phelps引理.%Phelps' lemma is extended to bornological vector spaces. An immediate application is to re-establish Wong's generalization of Ekeland variational principle to bornological vector spaces. And Ng and Zheng's result on existence of efficient points in topological vector spaces is easily achieved. Meanwhile, a Phelps' lemma in locally convex spaces is obtained.