T-凸空间中的KKM引理及其应用  

KKM Lemma and Its Applications on T-Convex Spaces

作　　者：陈治友[1] 

机构地区：[1]贵阳学院数学与信息科学学院,中国贵阳550005

出　　处：《湖南师范大学自然科学学报》2017年第5期84-87,共4页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(11561013);贵州省科技基金资助项目(黔科合J字[2014]2005);贵州省科技合作计划资助项目(黔科合LH字[2015]7298);贵州省科技厅联合基金资助项目(黔科合J字LKG[2013]30;黔科合LH字[2014]7176)

摘　　要：空间的凸性在非线性分析理论、变分不等式论以及最优化理论等领域扮演着重要角色.在这些领域中,不论是理论方面的问题,还是应用方面的问题,都依赖于空间的凸性.然而很多空间都不具备通常的以线性结构为基础的"凸性".在不具有线性结构的空间中,建立广义凸性,同时把连续选择定理、不动点定理以及其他重要结果推广到不依赖线性结构的广义凸性空间中具有十分重要的意义.为此,充分利用T-凸空间所满足的H_0-条件和经典的分析方法,在不具有线性结构的T-凸空间中,建立并证明KKM引理;同时借助该引理,给出一个不动点定理和一个不具拟T-凹性的函数的一个Ky Fan不等式的解的存在性定理.Convexity of spaces plays a very important role in non-linear analysis theory, variational inequality theory, optimal theory and so on. In all these cases of theoretical and applied studies, the dependence on the con-vexity of spaces is presumed. However, a lot of spaces do not possess the convex property from the viewpoint of the usual linear structure. Because of this, it has become recent interest to establish generalized convexity on spaces without linear structure and to generalize the continuity selection theorem, the fixed point theorem and some other important results, to generalized convex spaces. Here we make full use of the H0 -condition of T-convex space and classical analysis method, to prove KKM lemma on T-convex space without linear structure. Finally, we study two applications of this lemma on T-convex space. One is the fixed point theorem and the other is the existence theorem for the solution of Ky Fan inequality without quasi-T-concavity on T-convex spaces.

关 键 词：凸空间 条件 KKM引理 KYFAN不等式 

分 类 号：O177.3[理学—数学]