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．

Generalized Vector Quasi-Equilibrium Problems in Locally G-Convex Spaces

Some classes of generalized vector quasi_equilibrium problems (in short,GVQEP) are introduced and studied in locally G_convex spaces which includes most of generalized vector equilibrium problems, generalized vector variational inequality problems, quasi_equilibrium problems and quasi_variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G_convex spaces. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G_convex spaces. These results and argument methods are new and completely different from that in recent literature.