Differential Inequalities, Normality and Quasi-Normality
Complex Variables
2011-11-04 v1
Abstract
We prove that if D is a domain in C, alpha>1 and c>0, then the family F of functions meromorphic in D such that |f'(z)|/(1+|f(z)|^alpha)>c for every z in D is normalin D. For alpha=1, the same assumptions imply quasi-normality but not necessarily normality.
Keywords
Cite
@article{arxiv.1111.0844,
title = {Differential Inequalities, Normality and Quasi-Normality},
author = {Xiaojun Liu and Shahar Nevo and Xuecheng Pang},
journal= {arXiv preprint arXiv:1111.0844},
year = {2011}
}