摘要
给出平均一致凸Ｂａｎａｃｈ空间的定义，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中任意元在Ｘ的闭凸子集中存在唯一的最佳逼近元．
This paper introduced the definition of average uniform convex Banach spaceand proved the uniform convex space is the average uniform convex space. The average uniform convex space is reflexive space and weak local uniform convex space. The closed convexsubsets of the average uniform convex space X has one and only one best approximation forevery x∈X.
关键词
一致凸
平均一致凸
自反空间
巴拿赫空间
uniform convex space
average uniform convex Banach space
reflexivespace
weak local uniform convex space
