【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 .更多还原

【Abstract】 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.更多还原