抽象凸空间上的拟变分不等式及其应用  

Quasi-variational Inequality for Abstract Convex Spaces with an Application

作　　者：夏顺友[1,2] 

机构地区：[1]贵州大学计算机科学与技术学院,贵阳550025 [2]贵州师范学院数学与计算机科学学院,贵阳550018

出　　处：《应用数学学报》2014年第1期78-86,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11161008);贵州省科学技术基金(2012GZ71164)资助项目

摘　　要：为了得到不具线性结构的抽象凸空间上的非连续泛函的拟变分不等式解的存在性,首先,利用抽象凸空间上的KKM定理得到抽象凸空间上的弱Ky Fan不等式解的存在性,进而得到弱拟变分不等式和拟变分不等式解的存在性,作为推论,得到抽象凸空间上的Fan-GlicksbergKakutani不动点定理、Kakutani不动点定理和Tycholoff不动点定理.最后,作为应用给出了抽象凸策略空间上的n人非合作广义博弈Nash平衡点的存在性.In order to derive the existence of solution of quasi-variational inequality for functions with no continuity defined on abstract convex spaces with no linear structure. Firstly, by using KKM theorem in abstract convex space, the existence of solutions of Ky Fan inequality is proved. By the way, the existence of solutions of weakly quasi-variational inequality and quasi-variational inequality is derived. Furthermore, the Fan-Glicksberg- Kakutani fixed point theory, Kakutani fixed point theory and Tycholoff fixed point theory in abstract convex space, as corollaries, are derived. As an application, the existence of Nash equilibrium for n-person non-cooperative generalised game on abstract convex strategy spaces is established.

关 键 词：抽象凸空间 拟变分不等式 不动点定理 凡人非合作广义博弈 NASH平衡 

分 类 号：O177.9[理学—数学] O225[理学—基础数学]