Differential Inequalities, Normality and Quasi-normality

We prove that ifD is a domain in C,α 〉 1 and C 〉 0,then the family F of functions f meromorphic in D such that ｜f′（z）｜/1 ＋ ｜f（z）｜α 〉 C for every z ∈ D is normal in D.For α = 1,the same assumptions imply quasi-normality but not necessarily normality.

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 30; no. 2; pp. 277 - 282
Main Authors Liu, Xiao Jun, Nevo, Shahar, Pang, Xue Cheng
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2014
Springer Nature B.V
Subjects
Cgt
Functions (mathematics)
IFD
Mathematical models
Mathematics
Mathematics and Statistics
Science
Studies
Theorems
函数
定常态
微分不等式
Normal family
differential inequality
30D35
30A10
quasi-normal family
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Summary:We prove that ifD is a domain in C,α 〉 1 and C 〉 0,then the family F of functions f meromorphic in D such that ｜f′（z）｜/1 ＋ ｜f（z）｜α 〉 C for every z ∈ D is normal in D.For α = 1,the same assumptions imply quasi-normality but not necessarily normality.
Bibliography:11-2039/O1
We prove that ifD is a domain in C,α 〉 1 and C 〉 0,then the family F of functions f meromorphic in D such that ｜f′（z）｜/1 ＋ ｜f（z）｜α 〉 C for every z ∈ D is normal in D.For α = 1,the same assumptions imply quasi-normality but not necessarily normality.
Normal family, quasi-normal family, differential inequality
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-014-2542-8