| THE GROWTH THEOREM FOR STARLIKE MAPPINGS ON BOUNDED STARLIKE CIRCULAR DOMAINS |
| |
| 作者姓名： | Liu Taishun Ren Guangbin |
| |
| 作者单位： | LIU TAISHUN; (Department of Mathematics，University of Science and Technology of China，Hefei 230026，China)REN GUANGBIN; (Department of Mathematics，University of Science and Technology of China，Hefei 230026，China) |
| |
| 摘 要： | 1.IntroductionOnthegeometricfunctiontheoryofonecomplexvariable,thefollowinggrowthandi-coveringtheoremiswellknown(see2]).TheoremA.Foreachno~alizedunivalentjunctionfontheunitdiscDCC,ESPecially,theleft-handsideOftheaboveinequalityimpliesf(D)2ID.ForeachzED,z/0,equalityoccursintheaboveinequalityifandonlyiffisKoe6efunctionK(z)=theoritsrotatione--"K(e"z).Itisnaturaltoextendthisandotherresultsonthegeometricfunctiontheoryofonevariablestoseveralvariables.Butasearlyasfiftyyearsago,H.Cartanpointe…
|
| 关 键 词： | 星形映射 增长问题 循环域 单复变量 |
| 收稿时间： | 1996/10/24 0:00:00 |
THE GROWTH THEOREM FOR STARLIKE MAPPINGS
ON BOUNDED STARLIKE CIRCULAR DOMAINS |
| |
| Liu Taishun,Ren Guangbin.THE GROWTH THEOREM FOR STARLIKE MAPPINGS ON BOUNDED STARLIKE CIRCULAR DOMAINS[J].Chinese Annals of Mathematics,Series B,1998,19(4):401-408. |
| |
| Authors: | Liu Taishun and Ren Guangbin |
| |
| Institution: | DepartmentofMathematics,UniversityofScienceandTechnologyofChina,Hefei230026,China |
| |
| Abstract: | The authors obtain the growth and covering theorem for the class of normalized biholomorphic starlike mappings on bounded starlike circular domains.This type of domain discussed is rather general, since the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it. In the unit disc, it is just the famous growth and covering theorem for univalent functions.This theorem successfully realizes the initial idea of H. Cartan about how to extend geometric function theory from one variable to several complex variables. |
| |
| Keywords: | Starlike mappings Growth theorem Starlike circular domains |
| 本文献已被 CNKI 维普 等数据库收录！ |
| 点击此处可从《数学年刊B辑(英文版)》浏览原始摘要信息 |
| 点击此处可从《数学年刊B辑(英文版)》下载免费的PDF全文 |
