关于弱拟凸集与广义凸集逼近的几点注记

徐士英

系统科学与数学 ›› 1997, Vol. 17 ›› Issue (4) : 372-375.

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系统科学与数学 ›› 1997, Vol. 17 ›› Issue (4) : 372-375. DOI: 10.12341/jssms08349
论文

关于弱拟凸集与广义凸集逼近的几点注记

    徐士英
作者信息 +

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

    Xu Shiying;He Guolong
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文章历史 +

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.

Abstract

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]

关键词

弱拟凸集 / 最佳逼近 / 最佳联合逼近

Key words

Weak quasi convex set / best approximation / best simultaneous approximation

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徐士英. 关于弱拟凸集与广义凸集逼近的几点注记. 系统科学与数学, 1997, 17(4): 372-375. https://doi.org/10.12341/jssms08349
Xu Shiying. SOME REMARKS ON THE CHARACTERIZATION OF BEST APPROXIMATIONS FOR WEAK QUASI CONVEX SET. Journal of Systems Science and Mathematical Sciences, 1997, 17(4): 372-375 https://doi.org/10.12341/jssms08349
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