抽象凸度量空间上的R-KKM引理及其应用  

R-KKM Lemma with an Application in Abstract Convexity Metric Spaces

作　　者：夏顺友 王常春 杨彦龙[3] 陈治友[4] XIA Shun-you;WANG Chang-chun;YANG yan-long;CHEN Zhi-you(School of Mathematics and Big Data, Guizhou Education University, Guiyang 550018, China;Department of Mathematics, Zunyi Normal College, Zunyi Guizhou 563006, China;School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China;College of Mathematics and Information Science, Guiyang University, Guiyang 550005, China)

机构地区：[1]贵州师范学院数学与大数据学院,贵阳550018 [2]遵义师范学院数学学院,贵州遵义563006 [3]贵州大学数统学院,贵阳550025 [4]贵阳学院数学与信息科学学院,贵阳550005

出　　处：《西南师范大学学报（自然科学版）》2021年第3期96-100,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11561013,11761023,71961003);贵州师范学院博士基金项目(2018BS005);贵州省科技厅联合基金项目(黔科合LH字[2016]7031,[2017]7223号).

摘　　要：证明了满足广义KKM映射条件与H0条件的抽象凸度量空间的任意两个邻近对子集之间的集值映射的有限交性质.进一步,在紧性假设条件下,得到了该类集值映射的无限交性质.最后,证明了满足H0条件的抽象凸度量空间的任意两个邻近对子集之间的集值映射的最佳邻近点的存在性.We prove that each set-valued mapping between two proximity pairs subsets in abstract convexity metric spaces with condition of generalized KKM mappings and H 0 has the finite intersection property.Furthermore,the infinite intersection property is derived with compact conditions.Finally,existence of best proximity points is proved for every set-valued mappings between two proximity pairs subsets in abstract convexity metric spaces with H 0 condition.

关 键 词：抽象凸度量空间 广义KKM映射 邻近对 最佳邻近点 

分 类 号：O177.91[理学—数学]