赋范线性空间,normed linear space

1)normed linear space
赋范线性空间
1.
A kind of set-valued differential(γ-subdifferential) of functionals in normed linear space was defined,and its properties and application to nonsmooth multiobjective programming problem was discussed,so that some new results were obtained.
定义了赋范线性空间上泛函的一种新型集值导数(γ-次微分),讨论了它的一些性质及其在非光滑数学规划问题上的一些应用,得到了一些新的结果,这些结果改进和推广了已有的相关结论,对于进一步研究此问题提供了可靠的理论依据。


2.
In this paper,making use of hyperplane method,we improve the proof of the separation theorem;On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space.
在巴拿赫空间理论中,Hahn-Banach泛函延拓定理作为泛函分析三大基本定理之一,分隔性定理是Hahn-Banach定理的重要应用,本文利用"超平面"的方法,改进了一个分隔性定理的证明;另外,本文利用邻域的"平移"方法,给出了定义在赋范线性空间内的凸集上的次凸泛函连续性的简捷证明。


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2)Normed linear spaces
赋范线性空间
1.
Two theorem on Normed linear spaces;
赋范线性空间中的两个定理


2.
Moreover, the problem of approximating the fixed points of φ-hemicontractive mapping in normed linear spaces by the modified Ishikawa iterative sequences with errors is investigated.
进一步,还研究了赋范线性空间中φ-半压缩映象不动点的具误差的Ishikawa迭代逼近问题。


3.
Some properties of (f-) coapproximation and strongly (f-) coapproximation are studied in locally convex spaces and normed linear spaces.
研究了局部凸空间和赋范线性空间中的 (f_)共逼近和强 (f_)共逼近的一些性质 ,给出了f_共逼近、强f_共逼近和强f_Kolmogorov集的特征定理 ;并举例说明RaoGS的两主要定理是不正确的 ,同时作了相应的更正 。


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3)normed linear space
线性赋范空间
1.
In normed linear spaces,Ishikawa iterative sequence is used to provide three fixed point theorems.
在线性赋范空间中,应用Ishikawa迭代序列证明了3个不动点定理,这些定理也推广了PathakHK和KangSM等人的一些结果。


2.
In this paper,some properties of translation and application for ball in normed linear space are given.
给出了线性赋范空间中球的几个平移性质及其应用。


3.
This paper gives two characteristic property of the dependence of linear functionalon "dimX<+∞" in normed linear space.
本文给出了线性赋范空间中线性泛函与“dimX<+∞”有关的两个特征性质。



4)F-normed linear space
赋准范线性空间
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5)seminormed linear space
赋拟范线性空间
1.
Transferable conditions from metric linear space to F-normed and seminormed linear spaces;
距离线性空间成为赋准范、赋拟范线性空间的条件



6)Linear normed space
线性赋范空间
1.
Hua Luogeng s inequality is generalized in a linear normed space, and a parameter p in the oringinal inequality is increased to three parameters p,q and r , and our result is also a sharpened one for Hua s.
将华罗庚不等式推广到线性赋范空间 ,并且将原不等式的一个参数 p增加到三个参数 p ,q ,r ,所获结果也是对华罗庚不等式的加强 。




补充资料：赋范环


赋范环
u pauiioa

斌范环[.加挂dr血心;朋洲一Po.皿oe胶0叼o] l)与赋范代数或B田.山代数(助朋比al-罗腼)相同. 2)在其上有赎值(认公退加n)的环.葛显良译

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赋范线性空间,normed linear space