A KY FAN MATCHING THEOREM FOR TRANSFER COMPACTLY OPEN COVERS AND THE APPLICATION TO THE FIXED POINT

In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type fixed point theorem are obtained.     

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.     

非紧完备L-凸度量空间中的GLKKM定理及其对变分不等式和不动点的应用

In this paper, a new GLKKM type theorem is established for noncompact complete L-convex metric spaces. As applications, the properties of the solution set of variational in- equalities, intersection point sets, Ky Fan sections and maximal element sets are shown, and a Fan-Browder fixed point theorem is obtained.     

A Fixed Point Theorem and Some Generalized Ky Fan＇s Minimax Inequalities

In this paper, we establish a fixed point theorem for set-valued mapping on a topological vector space without ＂local convexity＂. And we also establish some generalized Ky Fan＇s minimax inequalities for set-value vector mappings, which are the generalization of some previous results.     

Coincidence Point Theorems,Intersection Theorems and Saddle Point Theorems on FC-spaces

In this paper, we first give the definitions of finitely continuous topological space and FC-subspace generated by some set, and obtain coincidence point theorem, whole intersection theorems and Ky Fan type matching theorems, and finally discuss the existence of saddle point as an application of coincidence point theorem.     

Fan Ky不等式的一个新改进

利用Gram矩阵的正定性和可变单位向量建立了Fan Ky不等式的一个新的改进,并且建立了反向Fan Ky不等式.对于非奇异矩阵,得到了Fan Ky不等式以及反向Fan Ky不等式的推广.     

广义Ky Fan点的通有稳定性

得到一个广义的Ky Fan不等式,它以通常的Ky Fan不等式为特例.我们讨论了在一致度量诱导的拓扑结构和二元泛函上方图形的拓扑结构下广义Ky Fan不等式问题构成的空间M中,大多数(在Baire分类意义下)广义Ky Fan不等式问题的所有广义Ky Fan点都是稳定的.     

T-凸空间中Fan Ky点与Nash平衡点存在定理

充分利用KKM方法和经典的集值分析方法,在不具有线性结构的T-凸空间中,建立并证明了弱Fan Ky点存在引理,并借助该引理获得了两个Fan Ky点存在定理;最后,作为对Fan Ky点存在定理的应用,在T-凸策略空间中建立并证明了n人非合作博弈Nash平衡点存在定理.     

紧开覆盖的一个新的Ky Fan型匹配定理及其应用

建立了紧开覆盖的一个新的Ky Fan型匹配定理.作为应用,研究了Fan-Browder型重合定理、Ky Fan型最佳逼近定理、极大元定理及超凸空间中的定性对策和抽象经济的平衡存在定理.     

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.     

FC-度量空间中的匹配定理及其对抽象经济的应用

利用KKM技巧,建立了FC-度量空间中转移紧开值映射的Ky Fan匹配定理.作为应用,获得了FC-度量空间中的Ky Fan重合定理、定性对策和抽象经济的平衡存在定理.结论统一、改进和推广了一些近期文献的已知结果.     

On certain Matching Properties of Convex Sets

In this paper we use a fixed-point theorem of the Ky Fan typewhich is proved by J.-P. Aubin to give a common generalizationof two matching theorems of Ky Fan concerning closed coveringsof convex sets in topological vector spaces.     

Minimax theorems for scalar set-valued mappings with nonconvex domains and applications

In this paper, by virtue of the separation theorem of convex sets, we prove a minimax theorem, a cone saddle point theorem and a Ky Fan minimax theorem for a scalar set-valued mapping under nonconvex assumptions of its domains, respectively. As applications, we obtain an existence result for the generalized vector equilibrium problem with a set-valued mapping. Simultaneously, we also obtain some generalized Ky Fan minimax theorems for set-valued mappings, in which the minimization and the maximization of set-valued mappings are taken in the sense of vector optimization.     

Hölder Continuity for Solution Mappings of Parametric Non-convex Strong Generalized Ky Fan Inequalities

Abstract

This article focuses on a new approach to investigate the Hölder continuity for the solution mapping of a parametric non-convex strong generalized Ky Fan inequality. Based on a non-convex separation theorem, the union relation between the solution set of the parametric non-convex strong generalized Ky Fan inequality and the solution sets of a series of Ky Fan inequalities, is established. Without density results and any information on the solution mapping, a sufficient condition for the Hölder continuity of the solution mapping to the parametric non-convex strong generalized Ky Fan inequality is given by using the key union relation. Our method does not impose any convexity, monotonicity, and the single-valuedness of the solution mapping.     

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.     

H—空间的覆盖性质及其应用

我们得到了Ｈ－空间闭（开）覆盖性质的几个定理，改进和推广了Ｓｐｅｒｎｅｒ，Ｋｌｅｅ，Ａｌｅｘａｎｄｒｏｆｆ－Ｐａｓｙｎｋｏｆｆ，Ｂｅｒｇｅ，Ｇｈｏｕｉｌａ－Ｈｏｕｒｉ，Ｄａｎｚｅｒ－Ｇｒｕｎｂａｕｍ－Ｋｌｅｅ，Ｋｙ Ｆａｎ，ｓｈｉｈ－Ｔａｎ，Ｈｏｒｖａｔｈ和Ｌａｓｓｏｎｄｅ等人的相应结果。作为应用，我们对ｌ．ｃ．－空间内的下半连续集值映象证明了一个几站不动点定理并且推广吉洪诺夫不动点定理到ｌ．ｃ．     

Generalized Knaster–Kuratowski–Mazurkiewicz Theorem Without Convex Hull

In this paper, a new notion of Knaster–Kuratowski–Mazurkiewicz mapping is introduced and a generalized Knaster–Kuratowski–Mazurkiewicz theorem is proved. As applications, some existence theorems of solutions for (vector) Ky Fan minimax inequality, Ky Fan section theorem, variational relation problems, n-person noncooperative game, and n-person noncooperative multiobjective game are obtained.