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Zbl 1177.30032
Xu, Yan; Wu, Fengqin; Liao, Liangwen
Picard values and normal families of meromorphic functions.
(English)
[J] Proc. R. Soc. Edinb., Sect. A, Math. 139, No. 5, 1091-1099 (2009). ISSN 0308-2105; ISSN 1473-7124/e

Summary: Let $f$ be a transcendental meromorphic function on the complex plane $\mathbb C$, let $a$ be a non-zero finite complex number, and let $n$ and $k$ be two positive integers. In this paper, we prove that if $n\ge k+1$, then $f+a\big(f^{(k)}\big)^n$ assumes each value $b\in \mathbb C$ infinitely often. Also, the related normality criterion for families of meromorphic functions is given. Our results generalize the related results of {\it M. Fang} and {\it L. Zalcman} [Sci. China, Ser. A 51, No. 7, 1196--1202 (2008; Zbl 1158.30020)].
MSC 2000:
*30D30 General theory of meromorphic functions
30D35 Distribution of values (one complex variable)

Keywords: transcendental meromorphic function; normality criterion

Citations: Zbl 1158.30020

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