Banach空间中度量投影算子的性质

Properties of Metric Projection in Banach Spaces

本文在一定的Ｂａｎａｃｈ几何框架下讨论了度量投影算子的若干性质．先利用对偶映射给出了投影算子的几个等价条件，然后利用等价条件讨论了自反、光滑、严格凸Ｂａｎａｃｈ空间中度量投影算子的线性性质和投影算子在凸闭子集中的方向导数等性质．

In this paper,some proerties of metric projection are discussed in Banach spaces.At first,some equivalent conditions are proved by duality mapping.Then the linear property is studied in reflexive,smooth,rotund Banach spaces.It's shown the metric projection has directional derivative at every point of a closed convex subset in reflexive,smooth,rotund Banach spaces with H property.