Bull. Korean Math. Soc. 2017; 54(2): 593-605
Online first article March 13, 2017 Printed March 31, 2017
https://doi.org/10.4134/BKMS.b160205
Copyright © The Korean Mathematical Society.
Yuntong Li and Zhixiu Liu
Shaanxi Railway Institute, Nanchang Institute of Technology
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
2014; 51(3): 691-700
2019; 56(1): 45-56
2018; 55(6): 1845-1858
2018; 55(2): 469-478
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd