锥凸对称向量拟均衡问题解集的通有稳定性

数学物理学报 ›› 2010, Vol. 30 ›› Issue (4): 1006-1017.

锥凸对称向量拟均衡问题解集的通有稳定性

陈剑尘, 龚循华

南昌大学数学系南昌 |330031

收稿日期:2007-11-28 修回日期:2009-04-15 出版日期:2010-07-25 发布日期:2010-07-25
基金资助:
国家自然科学基金(10561007)和江西省自然科学基金(2008GZS0072)资助

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

CHEN Jian-Chen, GONG Xun-Hua

Department of Mathematics, Nanchang University, Nanchang 330031

Received:2007-11-28 Revised:2009-04-15 Online:2010-07-25 Published:2010-07-25
Supported by:
国家自然科学基金(10561007)和江西省自然科学基金(2008GZS0072)资助

摘要/Abstract

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.

关键词: 对称向量拟均衡问题, 锥凸映射, 通有稳定性

Abstract:

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.

Key words: Symmetric vector quasi-equilibrium problem, Cone-convex mapping, Generic stability

中图分类号:

58E35

陈剑尘, 龚循华. 锥凸对称向量拟均衡问题解集的通有稳定性[J]. 数学物理学报, 2010, 30(4): 1006-1017.

CHEN Jian-Chen, GONG Xun-Hua. Generic Stability of the Solution Set for Symmetric Vector Quasi-equilibrium Problems under the Condition of Cone-convexity[J]. Acta mathematica scientia,Series A, 2010, 30(4): 1006-1017.

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