normed linear spaces

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。

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。

Kakutani Fixed Point Theorem in Fuzzy Normed Linear Space;

在Fuzzy赋范线性空间上引入多值映射的闭性概念与半连续概念,并建立了此空间上的Kaku-tani不动点定理。

Compactness and Completeness of Fuzzy Normed Linear Space;

讨论了 Fuzzy赋范线性空间中准紧集、完备集及有界集间的关系 ;给出完备 Fuzzy赋范空间的闭球套定理与 Baire定理 ;刻画了有限维 Fuzzy赋范空间的特征。

Two theorem on Normed linear spaces;

赋范线性空间中的两个定理

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。

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 。

Let X be a real normed linear space and A:XD(A)→X be a K-positive definite operator,f∈R(K) be arbitrary.

设X为实赋范线性空间,A:X D(A)→X为K正定算子。

Equicontinuity for Families of Quasi-homogeneous Operators in Fuzzy Normed Linear Spaces;

模糊赋范线性空间中准齐性算子族的等度连续性

Convex Sets and Convexities in Random Normed Linear Spaces;

随机赋范线性空间中的凸集与凸性