Abstract
In this paper, we discuss the normality and shared values of meromorphic functions with differential polynomial. We obtain the main result: Let \(\mathcal {F}\) be a family of meromorphic functions in a domain D and k, q be two positive integers. Let \(P(z,w)=w^{q}+a_{q-1}(z)w^{q-1}+\cdots +a_{1}(z)w \) and \(H(f,f',\ldots ,f^{(k)})\) be a differential polynomial with \(\frac{\varGamma }{\gamma }|_H<k+1\). If \(P(z,f^{(k)})+H(f, f',\cdots ,f^{(k)})-1~\)has at most \(q(k+1)-1\) distinct zeros (ignoring multiplicity) for each function \(f\in \mathcal {F}, f(z)\ne 0\), then \(\mathcal {F}\) is normal in D. This result generalizes that of Chang [1].
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Acknowledgements
Thanks to the support by National Natural Science Foundation of China (No. 11271090) and of National Natural Science Foundation Guangdong Province (No. 2016A030310257 and No. 2015A030313346).
The authors would like to express their hearty thanks to Professor Fang Mingliang and Liao Liangwen for their helpful discussions and suggestions. This work was also supported by the Visiting Scholar Program of Chern Institute of Mathematics at Nankai University when the authors worked as visiting scholars.
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Cui, Lx., Yuan, Wj. (2019). Normality and Shared Values of Meromorphic Functions with Differential Polynomial. In: Cao, BY., Zhong, YB. (eds) Fuzzy Sets and Operations Research. ICFIE 2017. Advances in Intelligent Systems and Computing, vol 872. Springer, Cham. https://doi.org/10.1007/978-3-030-02777-3_28
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DOI: https://doi.org/10.1007/978-3-030-02777-3_28
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