T-凸空间中广义H_(0)-条件下的KKM定理  

KKM Theorems under Generalized H_(0)-condition in T-Convex Spaces

作　　者：王常春 陈治友[2] 夏顺友 张转周 许光俊 WANG Changchun;CHEN Zhiyou;XIA Shunyou;ZHANG Zhuanzhou;XU Guangjun(Department of Mathematics,Zunyi Normal College,Zunyi Guizhou 563006;College of Mathematics and Information Science,Guiyang University,Guiyang 550005;School of Mathematics and BigData,Guizhou EducationUniversity,Guiyang 550018,China)

机构地区：[1]遵义师范学院数学学院,遵义贵州563006 [2]贵阳学院数学与信息科学学院,贵阳550005 [3]贵州师范学院数学与大数据学院,贵阳550018

出　　处：《重庆师范大学学报（自然科学版）》2021年第1期55-59,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.71961003,No.11661084,No:11761023);贵州省科技厅科技合作计划(黔科合LH字No.[2016]7031);贵州省科技厅基础研究计划(黔科合基础No.[2017]1201);贵州师范学院博士基金(No.2018BS005)。

摘　　要：【目的】为了在不具有线性结构的T-凸空间中得到弱于H_(0)-条件的GH_(0)-条件下的KKM引理。【方法】利用非线性分析中关于度量以及从属于紧集的有限覆盖的单位分解构造辅助函数,并基于GH_(0)-条件的特征,构造复合函数。【结果】在弱于H_(0)-条件的GH_(0)-条件下建立了T-凸度量空间和T-凸拓扑空间中的KKM引理。【结论】在空间结构和凸结构条件较弱的情形下推广了KKM引理。[Purposes]To derive the KKM lemma in T-convex spaces without linearity structure under GH_(0)-condition weakened with H_(0)-condition.[Methods]Composition functions are constructed based on the characteristics of GH_(0)-condition,and by utilizing constructed auxiliary functions with respect to metric and subjecting to unit decomposition about finite covering of compact set.[Findings]The KKM lemma in T-convex metric spaces and T-covex topology spaces are constructed under GH_(0)-condition weakened with H_(0)-condition.[Conclusions]Generalized KKM lemmas are delivered under more weak condition of structures for space and convexity.

关 键 词：T-凸空间 H_(0)-条件 GH_(0)-条件 KKM定理 

分 类 号：O177.91[理学—数学]