FC-空间中的不动点定理及其对广义拟平衡问题系统的应用

建立了非紧FC-空间中弱转移紧开值映射的不动点定理,作为应用,获得非紧FC-空间中广义拟平衡问题系统的平衡存在定理.     

FC-度量空间中的Browder型不动点定理及其对一般拟平衡问题系统的应用

建立非紧FC-度量空间中转移紧开值映射的Browder型不动点定理.作为应用,获得非紧FC-度量空间中一般拟平衡问题系统的平衡存在定理.     

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-空间中广义KKM定理及对广义向量平衡问题的应用

在非紧FC-空间中证明了一些新的广义KKM型定理.作为应用,在非紧FC-空间中我们确立了一些新的对于广义向量平衡问题解的存在性定理.这些结果推广了文献中巳有的结论.     

FC-度量空间中新的不动点定理及其对变分不等式和鞍点的应用(英文)

在非紧FC-度量空间中建立了一个新的不动点定理.作为应用,获得了一个极大元定理,新建了FC-度量空间中的变分不等式和鞍点定理.     

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.     

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.     

乘积拓扑空间内的重合点组定理及应用(Ⅱ)

应用(Ⅰ)中得到的定义在非紧FC-空间的乘积空间上的两簇集值映射的重合点定理,在FC-空间内对矢量平衡问题组、不等式组和极小极大定理组建立了一些新的存在性定理．这些结果推广了最近文献中某些已知结果．．     

FC-空间中的Ky Fan匹配定理及其对极大极小不等式的应用

建立了FC-空间中弱转移紧开覆盖的匹配定理.作为应用,获得了FC-空间中的重合定理、不动点定理、极大元定理和极大极小不等式.我们的结论统一、改进和推广了一些近期文献的已知结果.     

FK-映射的匹配定理及其对约束多目标对策的应用

利用 KKM 技巧,建立了FC-空间中转移紧开值FK-映射的Ky Fan匹配定理.作为应用,获得了FC-空间中的Ky Fan重合定理、约束多目标对策的加权 Nash-平衡和Pareto-平衡的存在定理.     

Generalized KKM type theorems in FC-spaces with applications (II)

This paper is a continuum of the preceding paper of author. By applying a coincidence theorem in noncompact FC-space without any convexity structure due to author, a new KKM type theorem is first proved under noncompact setting of FC-spaces. The equivalent relation between the coincidence theorem and the KKM type theorem is also established. As applications of the KKM type theorem, we establish some new existence theorems of solutions for three classes of generalized vector equilibrium problems under noncompact setting of FC-spaces. These theorems improve and generalize many known results in literature.     

非紧超凸度量空间中的一个新的不动点定理及其对截口问题和相交问题的应用

In this paper, a new Browder fixed point theorem is established in the noncompact sub-admissible subsets of noncompact hyperconvex metric spaces. As application, a Ky Fan section theorem and an intersection theorem are obtained.     

Quasi-equilibrium problems with applications to infinite optimization and constrained games in general topological spaces

By applying a new Fan-Browder type fixed point point theorem due to author, an existence theorem of quasi-equilibrium problem is proved in general topological space. As applications, some existence theorems of solutions for noncompact infinite optimization problems and noncompact constrained game problems are obtained in general topological spaces. These theorems improve and generalize a number of important results in recent literature.     

非紧超凸度量空间中的极大元定理及其对极大极小问题和鞍点问题的应用

在非紧超凸度量空间中的非紧次允许子集中建立了一个极大元定理．作为应用,研究了Fan-Browder型不动点定理、KyFan极大极小不等式和鞍点定理．     

Collective fixed points, generalized games and systems of generalized quasi-variational inclusion problems in topological spaces

In this paper, by using a fixed point theorem for expansive set-valued mappings with noncompact and nonconvex domains and ranges in topological spaces due to the author, we first prove a collective fixed point theorem and an existence theorem of equilibrium points for a generalized game. As applications, some new existence theorems of solutions for systems of generalized quasi-variational inclusion problems are established in noncompact topological spaces. Our results are different from known results in the literature.     

非紧L-凸空间中的一个新的极大元定理及其对鞍点的应用(英文)

在非紧L-凸空间中建立一个新的极大元定理.作为应用,获得了非紧L-凸空间中的极大极小不等式和鞍点定理.     

The Study of Minimax Inequalities, Abstract Economics and Applications to Variational Inequalities and Nash Equilibria

In this survey, a new minimax inequality and one equivalent geometricform are proved. Next, a theorem concerning the existence of maximalelements for an LC-majorized correspondence is obtained.By the maximal element theorem, existence theorems of equilibrium point fora noncompact one-person game and for a noncompact qualitative game withLC-majorized correspondences are given. Using the lastresult and employing 'approximation approach', we prove theexistence of equilibria for abstract economies in which the constraintcorrespondence is lower (upper) semicontinuous instead of having lower(upper) open sections or open graphs in infinite-dimensional topologicalspaces. Then, as the applications, the existence theorems of solutions forthe quasi-variational inequalities and generalized quasi-variationalinequalities for noncompact cases are also proven. Finally, with theapplications of quasi-variational inequalities, the existence theorems ofNash equilibrium of constrained games with noncompact are given. Our resultsinclude many results in the literature as special cases.     

非紧超凸度量空间中的一个新的极大元定理及其对抽象经济的应用(英文)

在非紧超凸度量空间中建立了一个新的极大元定理.作为应用,获得了连续选择及其不动点定理和一个Browder-Fan不动点定理.最后,新建了非紧超凸度量空间中的定性对策和抽象经济的平衡点存在定理.     

非紧L-凸空间中新的Ky Fan匹配定理及其对一般拟平衡问题组的应用

In this paper, a new Ky Fan matching theorem is established in noncompact L-convex spaces. As applications, a fixed point theorem and equilibrium existence theorems for systems of general quasiequilibrium problems and systems of quasiequilibrium problems in noncompact L-convex spaces are obtained.     

Some applications of the Knaster-Kuratowski and Mazurkiewicz principle in hyperconvex metric spaces

In this paper, as applications of the Knaster-Kuratowski and Mazurkiewicz principle in the hyperconvex version, we obtain the Ky Fan type matching theorems for closed and open covers. As applications, some intersection theorems which are hyperconvex versions of corresponding results due to Alexandroff and Pasynkoff, Fan, Klee, Horváth, and Lassonde are established. Then, the Ky Fan type best approximation theorem and Schauder-Tychonoff fixed-point theorem (i.e., Fan-Glicksberg fixed-point theorem) for set-valued mappings in noncompact hyperconvex spaces are also given. Finally, we obtain a general form of the Browder-Fan fixed-point theorem for set-valued mappings in noncompact hyperconvex spaces. These results include corresponding results in the literature as special cases.