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.
出处
《应用数学》
CSCD
北大核心
2001年第1期47-51,共5页
Mathematica Applicata
