Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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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.

Normal families of meromorphic functions with multiple values

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