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Normal functions concerning derivatives and shared sets

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Abstract

Let f(z) be meromorphic in \({\varDelta }\), \(E_1=\{a_1, a_2, a_3\}\) and \(E_2=\{b_1, b_2, b_3\}\) be two sets in \({\mathbb {C}}\), \(k\in Z^+\). Suppose that \(f (z)\in E_1 \Leftrightarrow f^{(k)}(z) \in E_2\) and \(\max \limits _{0\le i\le k-1}|f^{(i)}(z)|=0\) whenever \(f (z)\in E_1\), then f(z) is a normal function.

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Acknowledgements

We thank the referee for his/her valuable comments and suggestions made to this paper. This work is partially supported by the National Natural Science Foundation of China (11501367, 61673257), the Natural Science Foundation of Shanghai (17ZR1419900)

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Authors and Affiliations

  1. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, 201620, China

    Qiaoyu Chen

  2. School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China

    Dongbing Tong

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  1. Qiaoyu Chen
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  2. Dongbing Tong
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Correspondence to Dongbing Tong.

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Additional information

This work is partially supported by the National Natural Science Foundation of China (11501367, 61673257), the Natural Science Foundation of Shanghai (17ZR1419900).

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Chen, Q., Tong, D. Normal functions concerning derivatives and shared sets. Bol. Soc. Mat. Mex. 25, 589–596 (2019). https://doi.org/10.1007/s40590-018-0210-1

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  • DOI: https://doi.org/10.1007/s40590-018-0210-1

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