Differential Inequalities, Normality and Quasi-normality

• Published in: Acta mathematica Sinica. English series Vol. 30; no. 2; pp. 277 - 282
• Main Authors: Liu, Xiao Jun, Nevo, Shahar, Pang, Xue Cheng
• Format: Journal Article
• Language: English
• 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

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.