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

作　　者：陈剑尘[1] 龚循华[1] 

机构地区：[1]南昌大学数学系,南昌330031

出　　处：《数学物理学报（A辑）》2010年第4期1006-1017,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(10561007);江西省自然科学基金(2008GZS0072)资助

摘　　要：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.

关 键 词：对称向量拟均衡问题 锥凸映射 通有稳定性 

分 类 号：O317[理学—一般力学与力学基础]