度量空间中拟双曲映射与拟相似映射的一个等价刻画  

An Equivalent Characterization of Quasihyperbolic Mappings and Quasisimilarity Mappings in Metric Spaces

作　　者：刘红军 杨倩 梁茜 LIU Hongjun;YANG Qian;LIANG Qian(School of Mathematical Sciences,Guizhou Normal University,Guiyang 550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵阳550025

出　　处：《重庆师范大学学报（自然科学版）》2023年第6期72-77,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金面上项目(No.11671057);贵州省科学技术基金(No.黔科合基础[2020]1Y003);贵州师范大学博士科研启动基金(No.11904/0517078)。

摘　　要：根据拟双曲映射和拟相似映射的基本概念及性质,刻画拟双曲映射和拟相似映射在度量空间中的等价问题。利用拟双曲度量作为研究的重要工具,结合最大伸缩和最小伸缩的概念与拟双曲映射之间的关系,得到了拟双曲映射和拟相似映射在度量空间中是等价的。研究结果表明:假设X是c_(1)-拟凸度量空间,Y是c_(2)-拟凸度量空间,且G?X和G′?Y是两个子区域。如果f:G→G′是一个同胚映射,则f是一个M-拟双曲映射当且仅当f和f^(-1)都是同胚(M_(1),q)-拟相似映射,其中■。Basing on the basic concepts and properties of quasihyperbolic mappings and quasisimilarity mappings,to describe the equivalence problem of quasihyperbolic mappings and quasisimilarity mappings in metric space.Using quasihyperbolic metric as main tool to study,the relation between the concepts of maximal stretching and minimal stretching and quasihyperbolic mappings is discussed.It is found that quasihyperbolic mappings and quasisimilarity mappings are equivalent in metric space.The result of research shows that:let be a quasiconvex metric space,Y be a c_2-quasiconvex metric space,and let G?X and G′?Y be two domains.Suppose that f:G→G′ is a homeomorphism,then f is a M-quasihyperbolic mapping if and only if fand f~(-1)are homeomorphism(M_1,q)-quasisimilarity mappings,where ■.

关 键 词：拟双曲度量 拟双曲映射 拟相似映射 度量空间 

分 类 号：O174.55[理学—数学]