1) closed convex subset
闭凸子集
1.
Let X be a uniformly convex Banach space, E a closed convex subset of X and let T be self map on E.
又若X是一致凸的Banach空间,E是X的闭凸子集,T:E→E为自映射,对任意x0∈E,定义序列xn+1=(1-cn)xn+cnTxn,则迭代序列{xn}n∞=1若收敛于p,则p∈F(T)。
2) close convex subset
闭凸子集
3) weakly closed convex set
弱闭凸集
4) closed convex set
闭凸集
1.
Then,three equivalent theorems of continuous parameter set valued submartingale is proved:(1)L 1 wkc (X) valued submartingale is equal to ∫ ΩF τ 1 d p∫ ΩF τ 2 d p for any τ 1,τ 2∈T and τ 1<τ 2;(2)L 1 fc (X) valued submartingale is equal to S 1 F s (F s)cl{E(g/F s);g∈S 1 F t (F t)} for any s,t∈R + and s<t;(3)When X is separable,closed convex set valued subm.
继而证明了连续参数集值下鞅的三个等价定理：（ａ）Ｌ１ｗｋｃ（Ｘ）值下鞅等价于任给τ１＜τ２，τ１，τ２∈Ｔ，∫ΩＦτ１ｄＰ∫ΩＦτ２ｄＰ；（ｂ）Ｌ１ｆｃ（Ｘ）值下鞅等价于任给ｓ，ｔ∈Ｒ＋，ｓ＜ｔ，Ｓ１Ｆｓ（Ｆｓ）ｃｌ｛Ｅ（ｇ｜Ｆｓ），ｇ∈Ｓ１Ｆｔ（Ｆｔ）｝；（ｃ）Ｘ可分时，闭凸集值下鞅等价于任给ｓ，ｔ∈Ｒ＋，ｓ＜ｔ，Ａ∈Ｆｓ，ｃｌ∫ＡＦｓｄＰｃｌ∫ＡＦｔｄＰ。
2.
Some important properties of multifacility location models are to be dealt with, and an optimality condition for multifacility location problem on a closed convex set is put forward.
主要讨论多场址模型的性质，并给出了闭凸集上多场址问题的最优性条件。
5) Feng-closed convex sets
冯-闭凸集
6) convex-closed set
凸闭集
1.
It is proved in this paper that, the reachable set of system, in which the state varible is linear and control varible is nonlinear, must be boundedly convex-closed set provided that the control domain is boundedly closed set.
严格证明了，当控制区域为有界闭集时，状态变量为线性而控制变量为非线性的系统的等时区域是有界凸闭集，从而用等时区域方法能彻底解决这类系统的时间最优控制问题。
补充资料：凸子集
凸子集
convex subset
凸子集〔阴犯xs汕set;.训叮俄洲祀哪~}，偏序集的 包含任意二劝七素a .b、同时也包含整个区间(见区间与线段(Interval and segment))!a .b}的子集. 几A CKoPll删。撰I补注】一个不涉及区间概念的定义是:偏序集的子集A是凸的，若a延b簇c，侧.“，C任，4，则b任东 在实直线上(带有通常的序)，凸子集正是连通子集(按通常的拓扑).这对于更一般的有)神i扑空间((1rd已 redtopologi以1 sPa份)不一定成饭但如果给偏序集以区间拓扑(见序拓扑(order topology))，则连通子集是凸子集.戴执中译
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