非紧广义凸空间内的拟平衡问题

利用作者得到的一个新的不动点定理,在非紧广义凸空间内证明了拟平衡问题的几个新的平衡存在性定理.这些定理改进和推广了最近文献中许多已知结果.     

广义凸空间内的拟平衡问题和约束多目标对策

在没有线性结构的广义凸空间内研究了一类拟平衡问题和一类约束多目标对策.首先在非紧广义凸空间内对拟平衡问题证明了两个解的存在性定理.然后作为拟平衡存在定理的应用,在广义凸空间内对约束多目标对策建立了几个加权Nash-平衡和帕雷多平衡存在定理.这些定理改进、统一和推广了最近文献中多目标对策的相应结果.     

局部G-凸空间内的广义矢量拟平衡问题

在局部G-凸空间内引入和研究了几类广义矢量拟平衡问题(GVQEP)．包含了大多数广义矢量平衡问题,广义矢量变分不等式问题,拟平衡问题和拟变分不等式问题作为特殊情形．首先在局部G-凸空间内对一人对策证明了一个平衡存在性定理．作为应用,在非紧局部G-凸空间内对GVQEP的解建立了某些新的存在定理．这些结果和论证方法与最近文献中的结果和论证方法相比较是新的和完全不同的．     

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.     

乘积G-凸空间内的非空交定理和广义矢量平衡问题组

利用作者在G-凸空间内对集值映象簇得到的一个极大元存在性定理,在非紧乘积G-空间内,对集值映象簇建立了某些新的非空交定理．作为应用, 在非紧乘积G-凸空间内, 对广义矢量平衡问题组证明了一些平衡存在性定理．这些定理统一、改进和推广了文献中一些重要的已知结果．     

L-凸空间中的L_S优化映象的广义博弈均衡存在定理

在L-凸空间中,证明了定性博弈和广义博弈的均衡存在定理.     

局部FC-一致空间内具有联立广义矢量拟平衡组约束的数学规划(英文)

在局部FC-一致空间内引入和研究了某些新的联立广义矢量拟平衡问题组和具有联立广义矢量拟平衡组约束的数学规划.应用作者在局部FC-一致空间得到的Himmelberg型不动点定理,首先在局部FC-一致空间内对联立广义矢量拟平衡问题组的解证明了某些新的存在性定理.作为应用,对具有联立广义矢量拟平衡组约束的数学规划的解得到了某些新的存在性定理.     

局部FC-一致空间内的广义矢量拟变分包含组和广义矢量拟优化问题组

在没有凸性结构的局部FC-一致空间内,引入和研究了某些新的广义矢量拟变分包含问题组和广义矢量理想(真,帕雷多(Pareto),弱)拟优化问题组.应用KKM型定理和Himmelberg型不动点定理,首先对广义矢量拟变分包含问题组的解,证明了某些新的存在性定理.作为应用,对广义矢量理想(真,帕雷多,弱)拟优化问题组的解也得到了某些新的存在性结果.     

L-凸空间中一个新的GLKKM定理及其对带上下界的广义平衡问题的应用(英文)

在非紧L-凸空间中建立了一个新的GLKKM定理。作为应用,获得了带上下界的广义平衡问题的解的存在定理.     

乘积拓扑矢量空间中的不动点定理和广义矢量平衡问题组

利用零调映象的一个不动点定理,在乘积拓扑矢量空间内得到了某些新的不动点定理,作为应用,在乘积拓扑矢量空间内,对一类广义矢量平衡问题组证明了一些平衡存在性定理,这些定理推广了近期文献中的一些重要的已知结果.     

System of Generalized Vector Quasi-Equilibrium Problems in Locally FC-Spaces

A new class of locally finite continuous topological spaces （for short, locally FC-spaces） and a class of system of generalized vector quasi-equilibrium problems are introduced. By applying a generalized Himmelberg type fixed point theorem for a set-valued mapping with KKM-property due to the author, a collectively fixed point and an equilibrium existence theorem of generalized game are first proved in locally FC-spaces. By applying our equilibrium existence theorem of generalized game, some new existence theorems of equilibrium points for the system of generalized vector quasi-equilibrium problems are proved in locally FC-spaces. These theorems improve, unify and generalize many known results in the literatures.     

Generalized quasiconvexities,cone saddle points,and minimax theorem for vector-valued functions

We establish the following theorems: (i) an existence theorem for weak type generalized saddle points; (ii) an existence theorem for strong type generalized saddle points; (iii) a generalized minimax theorem for a vector-valued function. These theorems are generalizations and extensions of the author's recent results. For such extensions, we propose new concepts of convexity and continuity of vector-valued functions, which are weaker than ordinary ones. Some of the proofs are based on a few key observations and also on the Browder coincidence theorem or the Tychonoff fixed-point theorem. Also, the minimax theorem follows from the existence theorem for weak type generalized saddle points. The main spaces with mathematical structures considered are real locally convex spaces and real ordered topological vector spaces.This paper is dedicated to Professor Kensuke Tanaka on his sixtieth birthday.This paper was written when the author was a visitor at the Department of Mathematical Science, Graduate School of Science and Technology, Niigata University, Niigata, Japan. The author is indebted to Prof. K. Tanaka for suggesting this work.The author is very grateful to Prof. P. L. Yu for his useful encouragement and suggestions and to the referees for their valuable suggestions and comments.     

Existence of Solutions to a Generalized System

In this paper, we consider a generalized system in real Banach spaces. Using Brouwer’s fixed-point theorem, we establish some existence theorems for generalized system without monotonicity. Further, we extend the concept of C-strong pseudomonotonicity for a bifunction and extend Minty’s lemma for a generalized system. Furthermore, using the Minty lemma and KKM-Fan lemma, we establish an existence theorem for a generalized system with monotonicity in real reflexive Banach spaces.     

局部FC-一致空间内的广义约束多目标对策

在没有任何凸性结构的局部FC-一致空间内引入和研究了一类新的广义约束多目标对策,其中局中人数可以是有限或无限的和所有的支付函数可以取值于无限维空间．利用在局部FC-一致空间内得到的一个Himmelberg型不动点定理,在局部FC-一致空间内对广义约束多目标对策建立了某些弱Pareto平衡存在性定理．这些定理改进,统一和推广了最近文献中相应结果．     

Existence Theorems of Solutions for Generalized Quasi-variational Inequalities, a Minimax Theorem, and a Section Theorem in the Spaces without Linear Structure

In this paper, by using particular techniques, two existence theorems of solutions for generalized quasi-variational inequalities, a minimax theorem, and a section theorem in the spaces without linear structure are established; and finally, a new coincidence theorem in locally convex spaces is obtained.     

Generalized Variational-Like Inequalities with Nonmonotone Set-Valued Mappings

In this paper, we introduce a new class of generalized variational-like inequalities involving a nonmonotone-type set-valued mapping which is more general than those in the known literature. By applying a KKM-type theorem established by the author, some existence theorems for the solutions to the class of generalized variational-like inequalities are proved in Hausdorff locally convex topological vector spaces.     

Generalized KKM-type theorems for weakly generalized KKM mapping with some applications

In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.