Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications(Ⅰ)  

作　　者：丁协平 

机构地区：[1]College of Mathematics and Software Science,Sichuan Normal University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2007年第12期1561-1568,共8页应用数学和力学（英文版）

基　　金：the Natural Science Foundation of Sichuan Education Department of China (Nos.2003A081 and SZD0406)

摘　　要：First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.

关 键 词：condensing set-valued mapping maximal element generalized game equi-librium locally FC-uniform spaces 

分 类 号：O189[理学—数学]