有限连续拓扑空间上的相交定理和广义变分不等式

根据已知的FC-空间上的KKM型定理得出若干个相交定理,作为它们的应用,利用转移开闭映射的特征讨论广义变分不等式解的存在问题.本文的结果改进和推广了文献中的相应结论.     

FC-空间上的不动点定理和相交定理及其应用

介绍了没有凸结构和线性结构的有限连续拓扑空间(简称为FC-空间);得到了若干个非紧的FC-空间上不动点定理的开[闭]表现形式并建立了FC-空间上的连续选择定理.应用以上结果,在非常弱的假设下得出若干的相交定理和重合点定理,改进和推广了文献中的相应结果.     

聚合不动点定理及其对相交和变分不等式问题的应用

根据广义凸空间上的Fan-Browder型不动点定理得到在没有任何凸结构和线性结构和紧框架的拓扑空间的乘积空间上定义的Φ-映射族和弱Φ-映射族的聚合不动点定理,并作为应用,在非紧的拓扑空问上给出了相交定理和具有上下界的变分不等式问题的解的存在定理.     

一般化凸空间上的相交定理和一个不等式系

根据文[1]中得到的Ky Fan型重叠定理给出一般化凸空间上的相交定理.作为它的应用讨论一个不等式系的解的存在性问题.我们的结论改进和一般化了相应文献中的结果.     

FC-度量空间中新的不动点定理及其对鞍点的应用

利用KKM技巧,建立了FC-度量空间中转移紧开值映射的新的不动点定理.作为应用,获得了FC-度量空间中的极大元定理、相交定理、极大极小不等式和鞍点定理.我们的结论统一、改进和推广了一些近期文献的已知结果.     

FC-度量空间中的R-KKM定理及其对变分不等式和不动点的应用

引入了FC-度量空间,建立了非紧FC-度量空间中的R-KKM定理.作为应用,研究了非紧FC-度量空间中的变分不等式的解集、相交点集、Ky Fan截口和极大元集的性质,获得了FC-度量空间中的Fan-Browder不动点定理.     

FC-空间中的参数型KKM定理及其应用

首先在Fc-空间中证明了一个特征性质,然后通过引进线性序空间,利用集合的连通性,在非紧的FC-空间中证明了一个参数型KKM定理.应用参数型KKM定理得到非紧的极大极小不等式、鞍点定理和截口定理.这些结果改进和推广了这个领域中的一些相关结果.     

H-空间的截口定理重合定理相交定理及其应用*

本文的目的是在H-空间上得出几个截口定理、相交定理和重合定理.作为这些结果的应用,我们研究了H-空间中的极大极小不等式和变分不等式解的存在性问题.本文结果改进和发展了引文[1,3,5,6,8,9,12,14,15,17]中的相应结果.     

一般化凸空间上的截口定理和变分不等式定理

摘要：本文利用Brouwer不动点定理或已知的KKM型定理，得到一般化凸空间上的截口定理．讨论了变分不等式解的存在性问题。对文中的相应结论进行了一般化和改进。     

拓扑空间上的KKM定理,不动点定理,广义变分不等式

引进没有任何凸结构的拓扑空间上的广义R-KKM映射的定义并利用古典的KKM原理得到一般拓扑空间上的KKM型定理以及若干个变形结果,然后作为应用给出了非紧的拓扑空间上不动点定理和广义变分不等式解的存在性定理.     

From an abstract maximal element principle to optimization problems,stationary point theorems and common fixed point theorems

In this paper, we first establish an existence theorem related with intersection theorem, maximal element theorem and common fixed point theorem for multivalued maps by applying an abstract maximal element principle proved by Lin and Du. Some new stationary point theorems, minimization problems, new fixed point theorems and a system of nonconvex equilibrium theorem are also given.     

A Topological Intersection Theorem with Applications in H-Spaces

In this paper, a topological intersection theorem of a family of sets with H-convex sections is established. As an application to this theorem, the Nash equilibrium of abstract economy, the Ky-Fan minimax theorem, and an existence problem of solution for quasi-variational inequality are studied. The results presented in this paper modify and extend the corresponding results given in the literature.AMS Subject Classification (2000) 47H10This work is supported by the Foundation of Yunnan Science Technology Commission, China.     

Some existence theorems in nonlinear analysis for mappings on GFC-spaces and applications

We establish a maximal element theorem, an intersection theorem and a coincidence-point theorem in product GFC-spaces. As examples of wide ranges of applications, we first deduce sufficient conditions for the solution existence of a mixed system of inclusions. Then using this we obtain existence results for systems of vector quasi-optimization problems and for multiobjective mathematical programs constrained by systems of inclusions. Our results are shown to improve and include recent ones in the literature.     

Some existence theorems in nonlinear analysis for mappings on GFC-spaces and applications

We establish a maximal element theorem, an intersection theorem and a coincidence-point theorem in product GFC-spaces. As examples of wide ranges of applications, we first deduce sufficient conditions for the solution existence of a mixed system of inclusions. Then using this we obtain existence results for systems of vector quasi-optimization problems and for multiobjective mathematical programs constrained by systems of inclusions. Our results are shown to improve and include recent ones in the literature.     

Systems of nonempty intersection theorems with applications

In this paper, we study the systems of nonempty intersection theorems. By the systems of nonempty intersection theorems, we can study the existence theorem of systems of quasi-KKM problems, the existence theorems of systems of quasi-variational inclusions problems, the existence theorems of systems of quasi-variational disclusions problems, and fixed point theorem. We also establish some of their equivalent relations.     

Some fixed-point theorems and minimax inequalities in FC-space

By applying the existence theorem of maximal elements, some new collectively fixed-point theorems for a family of set-valued mappings defined on the product space of noncompact FC-space are proved and some new theorems about minimax inequality involving two functions are given to show the relations of fixed-point theorem and minimax inequality in FC-spaces. These results improve and generalize many important results in the recent literature.     

广义集值隐向量变分不等式问题系统解的存在性与稳定性

介绍了广义集值隐向量变分不等式问题系统,并且通过Kakutani-Fan-Glicksberg不动点定理,建立了其解的存在性结果;在此基础上,研究了广义集值隐向量变分不等式问题系统的稳定性,建立了其解集本质连通区的存在性结果.     

变分不等式问题的一个新的存在性定理

对于具有一般非空闭凸集约束的变分不等式问题 ,本文给出了一个新的例外族的定义 .通过倩同伦不变定理 ,我们证明了一个择一定理 ,这给出了所考虑问题解的一个充分性条件 .特别 ,我们建立了变分不等式问题的一个新的存在性定理 ,推广了Zhao的一个最近的存在性结果 ,进而也推广了著名Mor啨关于非线性互补问题的存在性定理 .