FC-空间上的不动点定理和极大极小定理  

Fixed point theorem and minimax theorems on FC-spaces

作　　者：朴勇杰[1] 河美兰[1] 

机构地区：[1]延边大学理学院,吉林延吉133002

出　　处：《辽宁师范大学学报（自然科学版）》2007年第4期397-400,共4页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10361005);延边大学科研项目(2004;No.8)

摘　　要：首先介绍了没有凸结构和没有线性结构的有限连续拓扑空间(简称,FC-空间)的概念,并给出了已有的FC-空间上的KKM型定理,然后根据该结果得到了非紧致的FC-空间上相交定理和不动点或平衡点存在定理,最后作为应用给出极大极小不等式定理.我们的结论推广和改进了H-空间,G-空间上的相应结果.The concept of the finite continuous topological space （simply ,FC-space ） without convex and linear structure was introduced firstly in this paper, and the well known KKM type theorem on non--compact FC-spaces was given,and then from which,intersection theorem and the existence theorem of fixed point or equilibrium point were derived, and finally minimax inequality theorems were given as applications. Out main results generalize and improve the corresponding results in H-space and G-space.

关 键 词：FC-空间 FC-子空间 KKM映射 下[上]半连续 不动点 平衡点 极大极小不等式 

分 类 号：O177.91[理学—数学] O189.1[理学—基础数学]