A Criterion of Normality Concerning Holomorphic Functions Whose Derivative Omit a Function II |
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Authors: | Qiaoyu CHEN and Xiaojun LIU |
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Institution: | 1. Department of Mathematics, East China Normal University, Shanghai 200241, China 2. Department of Mathematics, University of Shanghai for Science and Technology, Shanghai 200093,China |
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Abstract: | The authors discuss the normality concerning holomorphic functions and get the following result. Let F be a family of functions holomorphic on a domain D ? ?, all of whose zeros have multiplicity at least k, where k ?? 2 is an integer. Let h(z) ? 0 and ?? be a meromorphic function on D. Assume that the following two conditions hold for every f ?? F: $$ \begin{gathered} (a)f(z) = 0 \Rightarrow |f^{(k)} (z)| < |h(z)|. \hfill \\ (b)f^{(k)} (z) \ne h(z). \hfill \\ \end{gathered} $$ Then F is normal on D. |
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Keywords: | Normal family Meromorphic functions Omittcd function |
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