关于平均一致凸Banach空间

THE AVERAGE UNIFORMLY CONVEX BANACH SPACES

引入平均一致凸Ｂａｎａｃｈ空间的概念，证明了一致凸Ｂａｎａｃｈ空间是平均一致凸Ｂａｎａｃｈ空间，平均一致凸Ｂａｎａｃｈ空间是自反和弱局部一致凸Ｂａｎａｃｈ空间，并且平均一致凸Ｂａｎａｃｈ空间Ｘ中的任意元在Ｘ的闭凸子集中必存在唯一的最佳逼近元．

in this paper, the average uniform convexity of Banach spaces is introduced. We prove that uniformly convex spaces are average uniformly convex spaces, and average uniformly convex spaces are weak local uniformly convex and reflexive, and the closed convex subset of average uniformly convex space X has one and only one best approximation for every x ∈ X.