具有Q-正则*-断面的正则半群上的*-同余格

文中给出了一个具有正则*-断面正则半群的例子,该半群同时存在非平凡*-同余和非平凡的非*-同余;证明了正则*-断面上的每个*-同余都能扩张成整个半群上的*-同余;刻划了*-同余和*-同余格;定义了*-同余格上的两个完全同余T*FS和T*S*;研究了*-同余格上的完全同余T*S*, T*, T*l, Tr, U*和V*, 给出了这些同余的类中的极值同余(除U*, V*外).     

强P-正则半群上的最小正则＊-半群同余

主要研究了强P-正则半群S（P）上的最小正则＊-半群同余.利用S（P）的正则＊-断面S°得到S（P）上最小正则＊-半群同余的简单形式γP.由于S（P）/γP同构于S°,实质上S°是S（P）的最大正则＊-半群同态象,且S（P）的正则＊-断面不唯一,但从同意义上看正则＊-断面唯一.     

具有拟理想正则*-断面的正则半群

本文提出了具有正则*-断面正则半群的概念，所给出的例子表明具有拟理想正则*-断面的正则半群类真包含了具有拟理想逆断面的正则半群类和正则*-半群类；最后刻画了具有拟理想正则*-断面的正则半群的结构．     

集值映射的伪(*)连续与弱(*)连续性

本文引入了集值映射的伪（＊）连续性与弱（＊）连续性概念的定义,研究了伪（＊）连续、（＊）连续及弱（＊）连续的等价关系,最后研究了乘积空间中的集值映射成为伪（＊）连续和弱（＊）连续的充要条件。     

一致结构与一致覆盖族的非标准刻画

一致空间有三种等价描述方式,即通过满足各自条件的关系族,覆盖族和伪度量族.本文利用非标准分析的方法研究了一致空间,给出了一致结构与一致覆盖族的非标准刻画,并且利用（X×X）上的可滤单子化的等价关系构造了X上的一致结构.     

度量空间的序列商,k-映象

本文给出了度量空间序列商．肛映象的-些内部刻画。证明了空间X是度量空间的序列商。肛映象当且仅当X具有紧有限k-闭cs*-覆盖列的点星sn-网，当且仅当X具有紧有限k-闭覆盖列的点星网．作为上述结果的-个推论．不仅得到了空间X是度量空间序列商，k-映象当且仅当X是度量空间的k-映象，而且还证明了空间X是度量空间当且仅当X具有局部有限(紧有限)闭(肛闭)覆盖列的点星弱邻域网．这里“闭”(“k闭”)不能省略．     

关于Araki Elliott的定理1

在c~*-代数的定义中,要求范数是次乘的。但是这一点可以从其他条件推出来。 Araki-Elliott的定理1 设(A,||·||)是Banach空间,A并且是复数城上的*代数,及满足     

Toeplitz算子空间的ω~＊－闭包

本文讨论Ｔｏｅｐｌｉｔｚ算子空间的ω￣＊－闭包．我们证明Ｂｅｒｇｍａｎ空间上全体Ｔｏｅｐｌｉｔｚ算子的ω￣＊－闭包等于（定理１）．另外，我们给出Ｃ￣ｎ（ｎ＞１）中单位球面Ｓ上的Ｈａｒｄｙ空间Ｈ￣２（Ｓ）上的Ｔｏｅｐｌｉｔｚ算子的一个有趣刻划（命题２）．     

线性Ce^＊—半范数的次可乘性

证明了具有单位元的*-代数上的任何线性Ce^*-半范数（或具有自伴核的线性Ce0^*-半范数）一定是C^*-半范数。     

关于广义梯度＊弱上半连续的注记

在本文中，我们建立了集值映射的拟闭性和序列拟闭性的概念。在讨论巴拿赫空间上局部Ｌｉｐｓｃｈｉｔｚ函数的广义梯度的性质时，得到了集值映射ｘ→δｆ（ｘ）的＊弱上半连续与＊弱拟闭性等价的结果。并通过例子说明了＊弱拟闭性弱于ｘ弱序列拟闭性，从而改正了文（１）中的某些错误。     

Mazur交性质

主要考虑关于Mazur交性质的问题．我们通过赋范半群的对偶,给出了一个赋范空间只有平凡Mazur集白々等价刻画．另外,我们还讨论乘积空间对Mazur交性质的继承性,对Sersouri和Roy的结论作了一定的改进,将范数推广至更一般的情形．     

How to recognize nonexpansive mappings and isometric mappings

In two real Banach spaces, we shall present two conditions, under one of which each nonexpansive mapping must be an isometry.     

Strongly irreducible operators on Banach spaces

This paper firstly discusses the existence of strongly irreducible operators on Banach spaces. It shows that there exist strongly irreducible operators on Banach spaces with w*-separable dual. It also gives some properties of strongly irreducible operators on Banach spaces. In particular, if T is a strongly irreducible operator on an infinite-dimensional Banach space, then T is not of finite rank and T is not an algebraic operator. On Banach spaces with subsymmetric bases, including infinite-dimensional separable Hilbert spaces, it shows that quasisimilarity does not preserve strong irreducibility. In addition, we show that the strong irreducibility of an operator does not imply the strong irreducibility of its conjugate operator, which is not the same as the property in Hilbert spaces.     

Locally uniformly rotund points in convex-transitive Banach spaces

Almost transitive superreflexive Banach spaces have been considered in [C. Finet, Uniform convexity properties of norms on superreflexive Banach spaces, Israel J. Math. 53 (1986) 81–92], where it is shown that they are uniformly convex and uniformly smooth. We characterize such spaces as those convex transitive Banach spaces satisfying conditions much weaker than that of uniform convexity (for example, that of having a weakly locally uniformly rotund point). We note that, in general, the property of convex transitivity for a Banach space is weaker than that of almost transitivity.     

度量空间和锥度量空间中的若干不动点定理

给出了度量空间和锥度量空间中的若干不动点定理.利用这些不动点定理,统一并推广了度量空间和锥度量空间中的若干经典的不动点定理.     

The Solvability of Nonlinear Split Ordered Variational Inequality Problems in Partially Ordered Vector Spaces

The concept of nonlinear split ordered variational inequality problems on partially ordered Banach spaces extends the concept of the linear split vector variational inequality problems on Banach spaces, while the latter is a natural extension of vector variational inequality problems on Banach spaces. In this article, we prove the solvability of some nonlinear split vector variational inequality problems by using fixed-point theorems on partially ordered Banach spaces. It is important to notice that in the results obtained in this article, the considered mappings are not required to have any type of continuity and they just satisfy some order-monotonic conditions. Consequently, both the solvability of linear split vector variational inequality problems and vector variational inequality problems will be immediately obtained from the solvability of nonlinear split vector variational inequality problems. We will apply these results to solving nonlinear split vector optimization problems. The underlying spaces of the considered variational inequality problems may just be vector spaces which do not have topological structures, the considered mappings are not required to satisfy any continuity conditions, which just satisfy some order-increasing conditions.     

度量空间中有限点集的费马点

本文首先对紧致的度量拓扑空间证明了有限点集的费马点是存在的，其次，运用度量几何的经典方法考察了度量空间（包括双曲空间和Ｂａｎａｃｈ空间）中有限点集的费马点的唯一性，此外，还对ｎ维欧氏空间Ｅ＾ｎ中有限点集的费马作了进一步研究。     

广义度量S-KKM映射的性质及其对变分不等式的应用

引入了超S-γ-广义拟凸（凹）函数,建立了广义度量S-KKM映射与超S-γ-广义拟凸（凹）函数的关系.作为应用,获得了超凸度量空间中的新的KyFan极大极小不等式和鞍点定理.     

A Method Which Generates Splines in H-Locally Convex Spaces and Connections with Vectorial Optimization

In this research paper we present a modality for generating splines in H-locally convex spaces which allows us to solve some problems of best approximation by linear subspaces of spline functions in these spaces. In this way one shows that the elements of best vectorial approximation coincide with the spline functions introduced by us in a previous research work. These splines are also the only elements of best simultaneous approximation by their generated linear subspaces with respect to any family of seminorms which induces the H-locally convex topology and, consequently, they are the only solutions for some frequent strong and vectorial optimization programs. Moreover, as we shall see in the numerical examples, our construction leads to discover orthogonal decompositions for H-locally convex spaces which, in general, are difficult to be identified.     

Fixed point theory in Fréchet spaces for Volterra type operators

New fixed point theorems for maps (single and multivalued) between Fréchet spaces are presented. The proof relies on fixed point theory in Banach spaces and viewing a Fréchet space as the projective limit of a sequence of Banach spaces.