1) strongly extremely rotund
强极严格凸
1.
In this paper, we will give the cherecterizations of strongly extremely rotundity and strongly extremely smoothness in substitution spaces P XX n.
本文主要给出置换空间ＰＸＸｎ中强极严格凸与强极光滑性的特征。
2) strongly strictly convex
强严格凸
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) K-uniform(strong 、strict) convexity
K 一致(强、严格)凸
4) strictly strongly preinvex function
严格强预不变凸函数
5) semitrictly strongly preinvex function
半严格强预不变凸函数
6) strictly convex
严格凸
1.
In strictly convex Banach space,there is set F(T) of coupled fixed points of T for nonexpansive mapping,and it is a closed convex set.
在严格凸Banach空间中研究了非扩张映象T的耦合不动点集F(T)的闭凸性,获得了当F(T)是Hilbert空间中的闭线性子空间时,Ishikawa迭代的极限元与其初始元的最佳逼近元之间的关系。
2.
By using the renorming of Banach space, it was proved that every Banach space has an equivalent norm which is not strongly rough, and every Banach space has an equivalent norm which is not even, and every real Banach space has an equivalent norm ‖| · ‖| , such that ( X , ‖| · ‖| ) is not strictly convex or smooth.
应用再赋范方法，得到了任意Ｂａｎａｃｈ空间都存在不是粗的等价范数，任意Ｂａｎａｃｈ空间都存在不是平的等价范数等结论，证明了任意实Ｂａｎａｃｈ空间一定存在等价范数‖｜·‖｜，使得（Ｘ，‖｜·‖｜）既不是严格凸的，也不是光滑
3.
This paper uses uniform and simple form to treat uniformly convex, local uniformly convex, weak uniformly convex, weak local uniformly convex, strictly convex, (M) property and (WM) property in Banach space and an equivalence characterization of them in Banach space is given.
用统一且简洁形式处理Banach空间的一致凸、局一致凸、弱一致凸、弱局一致凸、严格凸及(M)性质和(WM)性质,给出了它们的一种等价刻画。
补充资料：凸凸
1.高出貌。
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