Dual Representations of Convex Sets and Gateaux Differentiability Spaces

The duality of two kinds of representations of convex sets is studied: the tangential representation of a convex body and the representations of its polar or negative polar by means of their weak^* exposed points. The equivalence of the representations is proved and a condition for their validity is obtained for individual sets (the case of arbitrary locally convex space) and for classes of sets (the case of Gâteaux differentiability locally convex space). Properties of Gâteaux differentiability locally convex spaces are studied and some examples of such spaces are given.     

p-距离空间中的一类压缩映象的不动点定理

仿照距离空间,2-距离空间中的一些概念,引入了p-距离空间及p-距离空间中的一些基本概念.根据研究2-距离空间中不动点理论的思想和方法,利用泛函分析的理论,对p-距离空间中的不动点问题进行了研究.把2.距离空间中压缩型映像的不动点理论移植到了p-距离空间中,形成了p-距离空间中压缩型映像的一些基本不动点理论.其距.离空...     

Contractibility and Connectedness of Efficient Point Sets

Using the technique of space theory and set-valued analysis, we establish contractibility results for efficient point sets in a locally convex space and a path connectedness result for a positive proper efficient point set in a reflexive space. We also prove a connectedness result for a positive proper efficient point set in a locally convex space; as an application, we give a connectedness result for an efficient solution set in a locally convex space.     

关于赋范空间上连续自映射的回归点

在赋范空间中讨论回归点的性质,主要得到了结果：（1）如果,是序列紧赋范空间X上的连续双射,x是f的任一回归点,则对于任意整数N〉0都存在f的回归点x0∈X使得f^n（x0）=x;（2）序列紧赋范空间上连续自映射的回归点集是f的强不变子集;（3）如果f是局部连通赋范空间X上的连续自映射,则f的每一个回归点或是类周期点或是类周期点的聚点．作为推论,在实直线段上得到了类似的结论．     

有限维赋范空间至C(Ω)-的等距逼近问题

本文讨论了有限维赋范空间Ｘ至无限维Ｃ（Ω）的等距逼近问题．证明了当Ｘ不是任意ｌ∞ｎ（ｎ∈Ｎ）的子空间且Ω中含无穷多个孤立点时，等距逼近问题不成立；在其它情形该问题都成立．     

The smallness problem for -algebras

Akemann showed that any von Neumann algebra with a weak^* separable dual space has a faithful normal representation on a separable Hilbert space. He posed the question: If a C^*-algebra has a weak^* separable state space, must it have a faithful representation on a separable Hilbert space? Wright solved this question negatively and showed that a unital C^*-algebra has the weak^* separable state space if and only if it has a unital completely positive map, into a type I factor on a separable Hilbert space, whose restriction to the self-adjoint part induces an order isomorphism. He called such a C^*-algebra almost separably representable. We say that a unital C^*-algebra is small if it has a unital complete isometry into a type I factor on a separable Hilbert space. In this paper we show that a unital C^*-algebra is small if and only if the state spaces of all n by n matrix algebras over the C^*-algebra are weak^*-separable. It is natural to ask whether almost separably representable algebras are small or not. We settle this question positively for simple C^*-algebras but the general question remains open.     

Properties of symmetric matrices

We find the extreme points and the smooth points of the unit ball of the Banach space n_℘ of all real symmetric (n×n)-matrices.     

On Kirk's asymptotic contractions

Recently Kirk introduced the notion of asymptotic contractions on a metric space and using ultrapower techniques he obtained an asymptotic version of the Boyd-Wong fixed point theorem. In this paper we extend this result and moreover, we give a constructive proof of it. Furthermore, we obtain a complete characterization of asymptotic contractions on a compact metric space. As a by-product we establish a separation theorem for upper semicontinuous functions satisfying some limit condition.     

偏序线性空间中向量集值映射最优化问题解的鞍点条件和Lagrange对偶

本文在没有任何拓扑结构的条件下，给出了向量集值映射最优化问题解的鞍点充分和必要条件以及Ｌａｇｒａｎｇｅ对偶，从而将文献（１）中的有关结果推广到更一般的偏序线性空间，并进一步给出了逆对偶定理。     

A fixed point approach to the stability of isometries

In this paper, we apply a fixed point theorem to the proof of Hyers-Ulam-Rassias stability property for isometries from a normed space into a Banach space, in which the parallelogram law holds.     

单位球面间的等距延拓

本文证明了在一定条件下赋范线性空间与其共轭空间的单位球面之间的等距算子可以延拓为全空间的实线性等距算子。进而,刻画了光滑的自反空间的单位球面到其共轭空间的单位球面上的等距算子。     

C·T·Yang‘s定理在模糊拓扑空间的推广

本文把点集拓扑学中的C·T·Yang定理推广到模糊拓扑学中 ,并且获得了一些其它新的结果     

关于非常圆的Banach空间

证明了非常圆空间的3个特征。讨论了非常圆空间和Banach空间几何性质之间的关系。建立了弱暴露点和Radon-Nikodym性质之间的联系。     

Fixed and periodic point theory in certain spaces

This paper proves the existence of periodic and fixed points for contractive conditions in metric (symmetric) space.     

A generalized section theorem and a minimax inequality for a vector-valued mapping 1

A generalized Fan's section theorem has proposed by replacing convexity assumptions with merely topological properties. A generalized reformulation of Browder's fixed point theorem has derived. The Minimax Inequalities for vector-valued mapping in an ordered Banach space have established without the convexity and with convexity, respectively.     

Stabilité de la Cohomologie LP au Voisinage de 2 pour les Espaces Localement Symétriques

We give a sufficient condition for stability around 2 of L^p cohomology of a system over locally symmetric space.     

Fixed point results on metric-type spaces

In this paper we obtain fixed point and common fixed point theorems for self-mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.     

FIXED POINT RESULTS ON METRIC-TYPE SPACES

In this paper we obtain fixed point and common fixed point theorems for self- mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.     

Linking in Hilbert space

We present the most general definition of the linking of sets in a Hilbert space and, drawing on the theory given in earlier papers by Schechter and Tintarev, give a necessary and sufficient geometric condition for linking when one set is compact.

     

用聚点研究函数有界性

在度量空间中,通过对函数在一个列紧集S的聚点附近的有界性讨论,给出了函数在整个点集S上有界性的判定方法.