关于弱拟凸集与广义凸集逼近的几点注记  

SOME REMARKS ON THE CHARACTERIZATION OF BEST APPROXIMATIONS FOR WEAK QUASI CONVEX SET

作　　者：徐士英[1] 何国龙[1] 

机构地区：[1]浙江师范大学基础数学研究所,金华321004

出　　处：《系统科学与数学》1997年第4期372-375,共4页Journal of Systems Science and Mathematical Sciences

摘　　要：本文证明了赋范线性空间中闭弱拟凸集必为凸集,并指出郭元明的”弱拟凸集的一些性质及其应用”、“广义凸集的联合逼近特性”两文中的主要结论实质上是已知的结果.This note concerns two papers by Guo Yuanming[1,2]. By introducing the concept of solar point, and by proving that each closed weak quasi-convex set must be convex in normed linear spaces, we point out that the main theorems contained in [1, 2] are in fact for the case where the approximate set is convex and thus are known results. Even more related results can be further improved to more general cases.

关 键 词：弱拟凸集 最佳逼近 最佳联合逼近 广义凸集 逼近 

分 类 号：O174.41[理学—数学]