Differential Inequalities, Normality and Quasi-Normality

Xiaojun Liu; Shahar Nevo; Xuecheng Pang

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arXiv · 1111.0844

Differential Inequalities, Normality and Quasi-Normality

Xiaojun Liu·Shahar Nevo·Xuecheng Pang

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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.

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BibTeX RIS

Xiaojun Liu, Shahar Nevo, Xuecheng Pang. 2011-11-03. Differential Inequalities, Normality and Quasi-Normality. https://arxiv.org/abs/1111.0844

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