Normal families of meromorphic functions with multiple values
Bull. Korean Math. Soc. 2017 Vol. 54, No. 2, 593-605
https://doi.org/10.4134/BKMS.b160205
Published online March 31, 2017
Yuntong Li and Zhixiu Liu
Shaanxi Railway Institute, Nanchang Institute of Technology
Abstract : In this paper, we consider some normality criteria concerning multiple values. Let $\mathcal{F}$ be a family of meromorphic functions defined in a domain $D$. Let $k$ be a positive integer and $\psi(z) \not \equiv 0,\infty$ be a meromorphic function in $D$. If, for each $f\in \mathcal{F}$ and $z\in D$, (1) $f(z)\neq 0$, and all of whose poles are multiple; (2) all zeros of $f^{(k)}(z)-\psi(z)$ have multiplicities at least $k+3$ in $D$; (3) all poles of $\psi(z)$ have multiplicities at most $k$ in $D$, then $\mathcal{F}$ is normal in $D$.
Keywords : meromorphic function, multiple value, normal family
MSC numbers : 30D45
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