Differential Inequalities, Normality and Quasi-normality - Liu, Xiao Jun; Nevo, Shahar; Pang, Xue Cheng (Acta mathematica Sinica. English series, 2014)
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.