远达函数的可导性与远达点的存在性

DERIVATIVES OF FARTHEST FUNCTIONS AND EXISTENCE OF FARTHEST POINTS

该文考察Ｂａｎａｃｈ空间上的远达函数的可导性与远达点的存在性间的关系，指出某些Ｂａｎａｃｈ空间上的远达函数（对有界闭集而言）具等于１或－１的单侧方向导数蕴含远达点的存在性，并给出了Ｂａｎａｃｈ空间ＣＬＵＲ和ＬＵＲ的新等价刻划．

The paper investigates the relationship between derivatives of farthest functions and existence of farthest points in Banach spaces.It is pointed out that the farthest distance function to a bounded closed set in a Banach space having a one side directional derivative equal to 1 or -1 implies the existence of farthest points.The new characterization theorems of (compact) locally uniformly convex Banach spaces are given.