复Banach空间中一类螺形映射子族的性质  

Properties of a subclass of spirallike mappings in complex Banach space

作　　者：张晓飞 ZHANG Xiaofei(School of Mathematics and Statistics,Pingdingshan University,Pingdingshan 467000,China)

机构地区：[1]平顶山学院数学与统计学院,河南平顶山467000

出　　处：《纯粹数学与应用数学》2023年第1期132-144,共13页Pure and Applied Mathematics

基　　金：国家自然科学基金(11701307);平顶山学院博士启动基金(PXY-BSQD-2015005);平顶山学院培养基金(PXY-PYJJ2016007).

摘　　要：首先定义了一个新的螺形映射子族S_(B)[β,A,B],其中β∈(−π/2,π/2),−1≤B<A≤1.然后利用Loewner理论给出了映射族S_(B)[β,A,B]在复Banach空间单位球上的增长定理和沿某单位方向的偏差定理.最后给出了欧氏空间单位球B^(n)上正规化双全纯映射族成为S_(B)[β,A,B]的充分条件.特别地,作为主要结果的应用,当β,A,B取某些特殊值时,可以很容易地得到一些熟知的结果.First,a new subclass of spirallike mappings S_(B)[β,A,B]is defined,whereβ∈(−π/2,π/2),−1≤B<A≤1.Then the growth theorem and distortion theorem along a unit direction for S_(B)[β,A,B]were obtained using the Loewner theory on the unit ball in complex Banach space.Finally,some sufficient conditions for normalized biholomorohic mappings to be S_(B)[β,A,B]were also characterized on the unit ball B^(n)in Euclidean space.In particular,as an application of the main results,whenβ,A and B takes some special values we can obtain some well-known results.

关 键 词：β型螺形映射 增长定理 偏差定理 

分 类 号：O174.56[理学—数学]