锥凸对称向量拟均衡问题解集的通有稳定性

Generic Stability of the Solution Set for Symmetric Vector Quasi-equilibrium Problems under the Condition of Cone-convexity

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.

In topological vector spaces, a new existence result on the weakly Pareto solutions for vector quasi-equilibrium problem is obtained by the Ky Fan＇s section theorem. As an application, a new existence theorem of the weakly Pareto solutions for symmetric vector quasi- equilibrium problem is obtained under the condition that its payoff functions are cone-convex. The theorem, under weaker conditions, solves the second problem proposed by Fu in [1], whether there is a weakly Pareto solution for symmetric vector quasi-equilibrium problem when its payoff functions are cone-convex. At last the authors discuss the generic stability of the solution set for symmetric vector quasi-equilibrium problem under the condition of cone-convexity in normed linear spaces.