凸性与度量投影的连续性  

Convexity and the Continuity of Metric Projections

作　　者：方习年[1] 王建华[2] 

机构地区：[1]安徽机电学院基础部,安徽芜湖241000 [2]安徽师范大学数学系,安徽芜湖241000

出　　处：《应用数学》2001年第1期47-51,共5页Mathematica Applicata

摘　　要：本文研究近强凸、近非常凸 Banach空间中度量投影的连续性 .获得如下结果 :若 A是近强凸 (近非常凸 )空间中的逼近凸集 ,则度量投影 PA是范 -范上半连续的(范 -弱上半连续的 ) .此外 ,我们还利用度量投影的连续性给出 Banach空间为近强凸、近非常凸的一些充分必要条件 .In this paper, we study the continuity of metric projections in nearly strong convex, nearly very convex Banach spaces. The following results are obtaited: Let A be a proximinal convex subset in a nearly strong convex (nearly very convex) Banach space, then the metric projection P A is norm norm upper semicontinous (norm weak upper semicontinous). Moreover, using the continuity of metric projections, we give some characterization of nearly strong convexity and nearly very convexity.

关 键 词：度量投影 逼近集 上半连续 近强凸 分离定理 凸性 BANACH空间 连续性 

分 类 号：O177.2[理学—数学]