Differential Inequalities, Normality and Quasi-Normality

Details Differential Inequalities, Normality and Quasi-Normality Differential Inequalities, Normality and Quasi-Normality

2011-11-03

arxiv.org/abs/1111.0844v1

Mathematics

Complex Variables

Scientific paper

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.

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