System of Generalized Vector Quasi-Equilibrium Problems in Locally FC-Spaces  

作　　者：Xie Ping DING 

机构地区：[1]College of Mathematics and Software Science, Sichuan Normal University Chengdu 610066, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2006年第5期1529-1538,共10页数学学报（英文版）

基　　金：This project is supported by the NSF of Sichuan Education Department of China (2003A081 and SZD0406)

摘　　要：A new class of locally finite continuous topological spaces （for short, locally FC-spaces） and a class of system of generalized vector quasi-equilibrium problems are introduced. By applying a generalized Himmelberg type fixed point theorem for a set-valued mapping with KKM-property due to the author, a collectively fixed point and an equilibrium existence theorem of generalized game are first proved in locally FC-spaces. By applying our equilibrium existence theorem of generalized game, some new existence theorems of equilibrium points for the system of generalized vector quasi-equilibrium problems are proved in locally FC-spaces. These theorems improve, unify and generalize many known results in the literatures.A new class of locally finite continuous topological spaces （for short, locally FC-spaces） and a class of system of generalized vector quasi-equilibrium problems are introduced. By applying a generalized Himmelberg type fixed point theorem for a set-valued mapping with KKM-property due to the author, a collectively fixed point and an equilibrium existence theorem of generalized game are first proved in locally FC-spaces. By applying our equilibrium existence theorem of generalized game, some new existence theorems of equilibrium points for the system of generalized vector quasi-equilibrium problems are proved in locally FC-spaces. These theorems improve, unify and generalize many known results in the literatures.

关 键 词：Generalized game System of generalized vector quasi-equilibrium problems KKM property Himmelberg type fixed point theorem Locally FC-space 

分 类 号：O17[理学—数学]