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| A Criterion of Normality Concerning Holomorphic Functions Whose Derivative Omit a Function II |
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Citation： |
Qiaoyu CHEN,Xiaojun LIU.A Criterion of Normality Concerning Holomorphic Functions Whose Derivative Omit a Function II[J].Chinese Annals of Mathematics B,2012,33(6):815~822 |
| Page view： 1953
Net amount： 1649 |
Authors： |
Qiaoyu CHEN; Xiaojun LIU; |
Foundation： |
the National Natural Science Foundation of China (No. 11071074) and the Outstanding Youth Foundation of Shanghai (No. slg10015). |
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| Abstract： |
The authors discuss the normality concerning holomorphic functions and get the following result. Let~$\mathcal {F}$~be a family of functions holomorphic on a domain $D \subset \mathbb{C}$, all of whose zeros have multiplicity at least~$ k$, where~$ k\geq 2 $ is an integer. Let~$ h(z)\not\equiv 0$ and $\infty$ be a meromorphic function on $D$. Assume that the following two conditions hold for every~$f \in\mathcal {F}:$${\rm(a)}~ f(z) = 0 \Rightarrow |f^{(k)}(z)| < |h(z)|$.${\rm(b)}~ f^{(k)}(z) \neq h(z). $ Then $\mathcal {F} $~is normal on $D$. |
Keywords： |
Normal family, Meromorphic functions, Omitted function |
Classification： |
30D35 |
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