1) local convex point
局部凸点
1.
In this paper,We first give a new definition,the local convex point.
本文给出了相对于凸分析中函数与集合整体性质的局部化,即定义了集合与函数的局部凸点,并且描述了该对象的性质,对已有结论进行了推广。
2) midpoint locally uniformly convex
中点局部一致凸
1.
It is shown that Banach space X is locally uniformly non square if and only if d X(x,1)>0 for all x∈S(X) ; X is strongly strictly convex if and only if whenver for any x∈S(X),y n∈S(X) and α∈R, if ‖x+αy n‖→0 , and ‖x-αy n‖→1, then α=0 ;and X is strongly strictly convex if and only if X is midpoint locally uniformly convex.
证明了Ｂａｎａｃｈ空间Ｘ是局部一致非方的当且仅当对任意ｘ∈Ｓ（Ｘ），都有ｄＸ（ｘ，１）＞０；Ｘ是强严格凸的当且仅当对任意ｘ∈Ｓ（Ｘ），ｙｎ∈Ｓ（Ｘ）和α∈Ｒ，若‖ｘ＋αｙｎ‖→１和‖ｘ－αｙｎ‖→１，则α＝０；并证明了Ｘ是强严格凸的充要条件为Ｘ是中点局部一致凸
3) local uniform convex point
局部一致凸点
1.
Lastly, it presents a necessary condition for local uniform convex point.
最后给出了局部一致凸点的一个必要条件。
4) compactly locally uniformly rotund points
紧局部一致凸点
5) compactly middle locally uniformly convexity
紧中点局部一致凸
1.
In this paper, a new geometric property is introduced,namely compactly middle locally uniformly convexity.
引入了一个新的几何性质，即紧中点局部一致凸性，给出了其与中点局部一致凸性的关系，并证明Orlicz空间具有紧中点局部一致凸性的等价条件是M∈△2且M∈SC。
6) midpoint locally K-uniform convexity
中点局部K一致凸性
1.
Midpoint locally uniform convexity is generalized to the midpoint locally K-uniform convexity,and the relation between the two cases is discussed.
主要研究的问题为:假定X、Y都具有中点局部一致凸性或中点局部K一致凸性,那么X pY(1
补充资料：局部
一部分；非全体：～麻醉 ㄧ～地区有小阵雨。
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