锥凸对称向量拟均衡问题解集的通有稳定性

在拓扑向量空间中,利用Ky Fan截口定理得到一个锥凸向量拟均衡问题弱Pareto解的存在性结果.作为该结果的应用,得到了一个对称向量拟均衡问题在支付映射为锥凸条件下弱Pareto解的存在性定理.该定理在较弱的条件下回答了Fu在文献[1]中提出的第二个问题,即在支付映射为锥凸且连续的条件下对称向量拟均衡问题的弱Pareto解是否存在.最后在赋范线性空间中研究了锥凸对称向量拟均衡问题弱Pareto解集的通有稳定性.     

拟变分包含系统(英文)

本文提出一些新的拟变分包含系统,利用向量映射的锥连续性与Park不动点定理,得到解的存在定理与解集的闭性.作为应用,得到对称强向量拟均衡问题与理想向量鞍点的存在性,推广与改进了近期的一些相关研究工作.     

具有控制结构的集值强向量均衡问题的稳定性

研究了具有控制结构的集值强向量均衡问题.通过Ky Fan截口定理得到了具有控制结构的集值强向量均衡问题解的存在性定理.并在映射满足一定条件的基础上,得到了集值强向量均衡问题所构成的空间M中,大多数(在Baire分类意义下)强向量均衡问题解集是稳定的.     

一类新型的广义向量拟均衡问题

提出一类新的广义向量拟均衡问题，并得到解的存在性定理．用于证明向量变分不等式和向量优化问题的解的存在性．     

具集值映射的广义强向量拟均衡问题

讨论了一类具集值映射的广义强向量拟均衡问题（GSVQEP）解的存在性.利用连续选择定理和不动点定理,在没有任何单调性假设下得到了GSVQEP解的存在性定理.     

隐式形式多值向量均衡问题解的存在性

考虑一类隐式形式多值向量均衡问题的解的存在性,该类问题包含了多值均衡问题、隐式向量均衡问题、多值变分不等式问题、向量变分不等式问题以及向量互补问题作为其特殊情形.利用广义Fan-Browder不动点定理,得到了拓扑向量空间中该类问题解的存要性定理,该结果推广并统一了已有问题解的存在性结果.     

W—空间的平衡问题

得到了Ｗ－空间数量情形的平衡问题的解的若干存在性定理,其结果在没有单调性条件下将文［１、２］的相应定理由Ｈａｕｓｄｏｒｆ拓扑向量空间推广到了Ｗ空间;然后通过引入ξ函数将其转化为向量形式,从而得到向量平衡问题的解的若干存在性定理,其结果在没有单调性条件下将文［１、３］的相应定理由Ｈａｕｓｄｏｒｆ拓扑向量空间推广到了Ｗ空间,且减弱了文［４、５］相应定理的连续性条件．     

对称向量拟均衡问题有效解的存在性

利用标量化方法建立对称向量拟均衡问题有效解的存在性定理。作为标量化方法的应用，利用这一方法得到向量变分不等式和拟向量变分不等式有效解的存在性定理。     

对称向量拟均衡问题与鞍点

提出一类新的对称向量拟均衡问题，证明其解的存在定理，并得到向量鞍点定理．本文是作者相关工作的继续．     

FC-空间中的不动点定理定理及应用

在FC-空间中建立了一个不动点定理,推广了近期文献的一个相关结论利用这个结果,我们建立了一些广义型定理,推广了著名的截口定理到FC-空间中借助这个截口定理,在FC-空间得到一些新的广义向量均衡问题解的存在性定理.     

一类集值映射的向量均衡问题

在拓扑向量空间内,研究了一类新的集值映射的广义向量均衡问题,利用KKM定理,证明了解的几个存在性定理,并讨论了解的性状.所得结果推广了近期一些作者的研究成果.     

Equilibrium problems and variational inequalities in topological vector spaces

An existence result for the equilibrium problem is proved in a general topological vector space. As applications, existence results are derived for variational inequality problems, vector equilibrium problems and vector variational inequality problems. Our results extend and unify a number of existence theorems in non-compact cases     

Gap Functions and Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems

This paper deals with generalized vector quasi-equilibrium problems. By virtue of a nonlinear scalarization function, the gap functions for two classes of generalized vector quasi-equilibrium problems are obtained. Then, from an existence theorem for a generalized quasi-equilibrium problem and a minimax inequality, existence theorems for two classes of generalized vector quasi-equilibrium problems are established. This research is partially supported by the Postdoctoral Fellowship Scheme of The Hong Kong Polytechnic University and the National Natural Science Foundation of China.     

On Generalized Vector Equilibrium Problems

A new generalized vector equilibrium problem involving set-valued mappings and the proper quasi concavity of set-valued mappings in topological vector spaces are introduced; its existence theorems and the convexity of the solution sets are established.     

Generalized vector quasi-equilibrium problems with applications

In this paper, we consider the generalized vector quasi-equilibrium problem with or without involving Φ-condensing maps and prove the existence of its solution by using known fixed point and maximal element theorems. As applications of our results, we derive some existence results for a solution to the vector quasi-optimization problem for nondifferentiable functions and vector quasi-saddle point problem.     

Stampacchia generalized vector quasi-equilibrium problem with set-valued mapping

In this paper, the solvability of Stampacchia generalized vector quasi-equilibrium problem (in short, GVQEP) with set-valued mapping is studied. By using continuous selection theorem and fixed point theorems, some existence theorems for (GVQEP) are obtained without any monotonicity assumption. These theorems unify and improve some results in the recent references.     

System of Generalized Vector Quasi-Equilibrium Problems with Applications to Fixed Point Theorems for a Family of Nonexpansive Multivalued Mappings

In this paper, we establish the existence theorems of the generalized vector quasi-equilibrium problems. From some existence theorem, we establish fixed point theorems for a family of lower semicontinuous or nonexpansive multivalued mappings. We also obtain the existence theorems of system of mixed generalized vector variational-like inequalities and existence theorems of the Debreu vector equilibrium problems and the Nash vector equilibrium problems.