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Normality and fixed-points of meromorphic functions - MaRDI portal

Normality and fixed-points of meromorphic functions (Q2368541)

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Normality and fixed-points of meromorphic functions
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    Normality and fixed-points of meromorphic functions (English)
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    21 April 2006
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    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 \textit{X. Pang} and \textit{L. Zalcman} in [Ark. Mat. 38, 171--182 (2000; Zbl 1079.30044)] a new and simplified proof concerning normality and shared values.
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    meromorphic function
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    normal family
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    shared value
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