Year: 2016
Author: Qiong Wang, Wenjun Yuan, Wei Chen, Honggen Tian
Communications in Mathematical Research , Vol. 32 (2016), Iss. 1 : pp. 88–96
Abstract
In this paper, we consider normality criteria for a family of meromorphic functions concerning shared values. Let $\mathcal{F}$ be a family of meromorphic functions defined in a domain $D, m, n, k$ and $d$ be four positive integers satisfying $m ≥ n + 2$ and $d ≥ \frac{k + 1}{m − n − 1}$, and $a(≠0), b$ be two finite constants. Suppose that every $f ∈ \mathcal{F}$ has all its zeros and poles of multiplicity at least $k$ and $d$, respectively. If $(f^n)^{(k)}−af^m$ and $(g^n)^{(k)}−ag^m$ share the value $b$ for every pair of functions $(f, g)$ of $\mathcal{F}$, then $\mathcal{F}$ is normal in $D$. Our results improve the related theorems of Schwick (Schwick W. Normality criteria for families of meromorphic function. $J$. $Anal$. $Math$., 1989, 52: 241–289), Li and Gu (Li Y T, Gu Y X. On normal families of meromorphic functions. $J$. $Math$. $Anal$. $Appl$., 2009, 354: 421–425).
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2016.01.07
Communications in Mathematical Research , Vol. 32 (2016), Iss. 1 : pp. 88–96
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: meromorphic function shared value normal criterion.