Generalized Bi quasi variational Inequalities in Locally Convex Topological Vector Spaces

In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence theorems of solutions for generalized bi quasi variational inequalities,which are the extension and improvements of the earlier and recent results obtained previously by many authors including Sun and Ding [18],Chang and Zhang [23] and Zhang [24].

COVERING PROPERTIES ON H-SPACES AND APPLICATIONS

Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbaum-Klee, Ky Fan, Shih-Tan, Horvath and Lassonde. As application an almost fixed point theorem for lower semi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed point theorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.

Robinson-Ursescu Theorem in p-normed Spaces

For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and the open mapping and closed graph theorems for closed convex set-valued maps.

Fuzzifying Topological Linear Spaces Based on Continuous-Valued logic

In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and the topological properties of fuzzifying convex set in the fuzzifying topological linear space.

On the Random Conjugate Spaces of a Random Locally Convex Module

Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally suitable for the current development of the theory of random conjugate spaces. In this process, we also obtain a somewhat surprising and crucial result： if the base （Ω,F, P） of a random normed module is nonatomic then the random normed module is a totally disconnected topological space when it is endowed with the locally L0-convex topology.

Linear Systems of a Class in a Locally Convex Space

In Refs. [1] and [2], the authors gave the solutions of linear systems of a class with ranges in a Banach space. In distributed parameter systems, because many spaces of the functions of solutions are not Banach spaces, we need extend the scope of the space to a locally convex space. Suppose that E is a complete separated locally convex space, E’ is the dual space of E, R^+ is a set of non-negative numbers, C is a set of all complex numbers, and P,

局部凸拓扑空间中的不动点定理与固有值

利用拓扑度理论讨论了局部凸拓扑向量空间中不动点定理和非线性算子固有值 ,从而推广了 [1]和[2 ]中的结果 。

局部凸拓扑空间中凝聚映象的不动点定理

利用拓扑度理论讨论了局部凸拓扑向量空间中凝聚映象的不动点问题,首先证明了凝聚映像中的Leray-Shauder定理,然后应用此定理在局部凸拓扑向量空间中进一步推广了Altman定理,从而获得了一些更为广泛的不动点定理,所得结果是已知结果的本质改进与推广.

完备稠序线性序拓扑空间上不稳定流形的边界点的周期性

研究完备稠序线性序拓扑空间上连续自映射的不稳定流形的结构.首先证明了连续自映射在不动点处的不稳定流形是连通的.然后指出连续自映射的周期点处的不稳定流形必是有限个区间的并.最后,利用所得结果证明了在具有最大最小元的完备稠序线性序拓扑空间上连续自映射的不稳定流形的边界如果不属于流形本身,则必为该连续自映射的周期点.

关于局部凸线性拓扑空间的几种凸性及光滑性

对局部凸线性拓扑空间引进了强凸和非常凸的概念，并讨论了这两种凸性与其它凸性之间的关系，此外，还引进了非常光滑和弱局部一致光滑的概念，并指出了非常光滑（弱局部一致光滑）是非常凸（弱局部一致凸）的共轭概念。

(C_0)类等度连续半群的无穷小生成元的特征

主要讨论在局部凸线性拓扑空间上的(C0)类等度连续半群{T(t):t≥0}诱导的C 0-半群拓扑意义下,{T(t):t≥0}的一些基本性质,以及(C0)类等度连续半群{T(t):t≥0}在C 0-半群拓扑意义下以及原拓扑意义下的无穷小生成元之间的关系.

拓扑空间上半连续函数的等价条件

首先给出了拓扑空间上网的上(下)极限和函数的上(下)极限的定义,以及一般拓扑空间到线性序拓扑空间的半连续函数的定义,然后得到了拓扑空间上函数连续和函数半连续的关系,最后证明了拓扑空间上函数半连续的几个等价条件.

序线性拓扑空间中的凸算子在矩阵极值中的应用

文［１］将Ｒｎ 中Ｋｕｈｎ－Ｔｕｃｋｅｒ的条件推广到了序线性拓扑空间中，文［６］从另一角度出发把著名的Ｊｅｎｓｅｎ 不等式推广到了序Ｂａｎａｃｈ 空间之中，本文在［１］，［６］启发之下，以锥为工具给出了序线性拓扑空间中的凸算子在矩阵极值中的某些应用，从而利用变分的方法得到了广义最小二乘解的一个新证明．

线性序拓扑空间上不稳定流形的映射性质

文章研究完备稠序的线性序拓扑空间上连续自映射f的不稳定流形。首先证明了不动点P的不稳定流形与P的任意邻域V的交集,通过f有限次迭代之后,会包含P的不稳定流形。然后利用此结果证明了f^k在p_i(1≤i≤k)的不稳定流形被f映射的象集合为f^k在f(p_i)的不稳定流形(其中p_i为f的k-周期轨上的点)。

半凸性与Fuzzy拓扑线性空间

本文引进了半凸fu=y集和局部半凸fu=y拓扑线性空间的概念,研究了它们的某些性质,借助于fu=y拟 p_■—范族(a∈Г.0<p_■≤1)给出了fu=y拓扑线性空间为局部半凸的一个充分必要条件。

局部凸拓扑向量空间中的不动点定理

把Altman定理推广到局部凸拓扑向量空间,并由此获得了一些更广泛的不动点定理.

局部凸I-拓扑线性空间的投影拓扑与投影极限

给出模糊线性序同态的某些性质。在此基础上,利用Katsaras意义下的局部凸I-拓扑线性空间概念的一个等价刻画,引进并研究了新的投影拓扑与投影极限,得到了与经典拓扑线性空间理论中相应定理相平行的结果,改进和推广了严从华的结论。

某些空间X的对偶X^＊可赋范的充要条件

证明了对赋可列半范的局部凸空间Ｘ而言（Ｘ不必自反），其强对偶空间Ｘ＊可赋范的充要条件是Ｘ可赋范．

拓扑向量空间中的一类平衡问题研究

通过对偶的方法研究了拓扑向量空间上的一类平衡问题,并详细的证明了平衡问题解的存在性结果,又利用集值映射的拟凸性讨论了一类集值映射的平衡问题,并给出了详细的证明过程,得到其平衡问题的解的存在性结果.

凸锥X^＊β中α—有界与γ—有界的等价性

在局部β－凸空间Ｘ中的连续β－次半范形成的凸锥Ｘ＊β上定义了两个一致收敛锥拓扑α－拓扑与γ－拓扑，并讨论了他们的有界性。