| 凸性与度量投影的连续性 |
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| 引用本文： | 方习年,王建华. 凸性与度量投影的连续性[J]. 应用数学, 2001, 14(1): 47-51 |
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| 作者姓名： | 方习年 王建华 |
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| 作者单位： | 1. 安徽机电学院基础部,
2. 安徽师范大学数学系, |
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| 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。
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| 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 |
| 文章编号： | 1001-9847(2001)01-0047-05 |
| 修稿时间： | 2000-03-23 |
Convexity and the Continuity of Metric Projections |
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| FANG Xi nian ,WANG Jian hua. Convexity and the Continuity of Metric Projections[J]. Mathematica Applicata, 2001, 14(1): 47-51 |
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| Authors: | FANG Xi nian WANG Jian hua |
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| Affiliation: | FANG Xi nian 1,WANG Jian hua 2 |
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| 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. |
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| Keywords: | Metric projection Proximinal set Upper semi continuous Nearly strong convex Separation theorem |
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