弱拟凸集的一些性质及其应用  

SOME PROPERTIES OF WEAKLY QUASICONVEX SETS AND THEIR APPLICATIONS

作　　者：郭元明[1] 

机构地区：[1]湖南教育学院数学系,长沙410012

出　　处：《系统科学与数学》1992年第1期30-34,共5页Journal of Systems Science and Mathematical Sciences

摘　　要：在文[1]中,我们提出了赋范线性空间中伪凸、弱拟凸等广义凸集的概念,并探究了其逼近性质.本文将给出[1]中所提出的广义凸集中最弱的一种集——弱拟凸集的最佳逼近特征、强唯一性及弱拟凸集的强分离定理.并把所获的结果应用到 L_p(T,m)空间中去,得到了 L_1(T,m)空间中最佳逼近的特征和唯一性及 L_p(T,m)(1<p≤2)空间中最佳逼近的强唯一性,这里(T,m)为正测度空间.In this paper,the approximation properties of weakly quasiconvex sets in normedlinear spaces are investigated.First,characterization and strong Uniqueness of bestapproximation are given when the approximating set is weakly quasiconvex,and aseparation theorem of weakly quasiconvex sets is obtained.Secondly,by use of theresults,characterization and uniqueness of best approximation in L_1(T,m) and stronguniqueness of best approximation in L_p(T,m)(1<p≤2) are obtained.

关 键 词：弱拟凸集 最佳逼近 强唯一性 分离 

分 类 号：O177.3[理学—数学]