DISTORTION THEOREMS FOR CLASSES OF g-PARAMETRIC STARLIKE MAPPINGS OF REAL ORDER IN C^(n)  

作　　者：刘红炎 涂振汉 熊良鹏 Hongyan LIU;Zhenhan TU;Liangpeng XIONG(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China;Jiangxi Science and Technology Normal University,Nanchang 330038,China)

机构地区：[1]School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China [2]School of Mathematics and Computer Science,Jiangxi Science and Technology Normal University,Nanchang 330038,China

出　　处：《Acta Mathematica Scientia》2023年第4期1491-1502,共12页数学物理学报（B辑英文版）

基　　金：the National Natural Science Foundation of China(12071354);XIONG was the National Natural Science Foundation of China(12061035);the Jiangxi Provincial Natural Science Foundation(20212BAB201012);the Research Foundation of Jiangxi Provincial Department of Education(GJJ201104);the Research Foundation of Jiangxi Science and Technology Normal University(2021QNBJRC003)。

摘　　要：In this paper,we define the class S_(g)^(BX)of g-parametric starlike mappings of real order γ on the unit ball BX in a complex Banach space X,where g is analytic and satisfies certain conditions.By establishing the distortion theorem of the Fr´echet-derivative type of S_(g)^(BX)with a weak restrictive condition,we further obtain the distortion results of the Jacobi-determinant type and the Fr´echet-derivative type for the corresponding classes(compared with S_(g)^(BX))defined on the unit polydisc(resp.unit ball with the arbitrary norm)in the space of n-dimensional complex variables,n≥2.Our results extend the classic distortion theorem of holomorphic functions from the case in one-dimensional complex space to the case in the higher dimensional complex space.The main theorems also generalize and improve some recent works.

关 键 词：Banach space distortion theorem of Jacobi-determinant type distortion theorems of the Frechet-derivative type g-parametric starlike mappings 

分 类 号：O177.2[理学—数学]