Normality and fixed-points of meromorphic functions. (English) Zbl 1095.30026

Chang, Jianming; Fang, Mingliang; Zalcman, Lawrence

Ark. Mat. 43, No. 2, 307-321 (2005).

The main result in the paper under review is the following: Let \(\mathcal F\) be a family of meromorphic functions on a domain \(\mathcal D\) in the complex plane \(\mathbb{C}\), and let \(R\) be a rational function with \(\text{deg}\;R\geq3\). If, for any \(f\in\mathcal F\), the composite function \(R(\mathcal F)\) has no fixed point in \(\mathcal D\), then \(\mathcal F\) is normal in \(\mathcal D\). Further, the authors give a result of X. Pang and L. Zalcman in [Ark. Mat. 38, 171–182 (2000; Zbl 1079.30044)] a new and simplified proof concerning normality and shared values.

Reviewer: Rauno Aulaskari (Joensuu)

MSC:

30D45	Normal functions of one complex variable, normal families
30D30	Meromorphic functions of one complex variable (general theory)

Keywords:

meromorphic function; normal family; shared value

Citations:

Zbl 1079.30044

References:

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