TY - JOUR
T1 - Normality Criteria of Meromorphic Functions
AU - Wang , Qiong
AU - Yuan , Wenjun
AU - Chen , Wei
AU - Tian , Honggen
JO - Communications in Mathematical Research 
VL - 1
SP - 88
EP - 96
PY - 2021
DA - 2021/03
SN - 32
DO - http://doi.org/10.13447/j.1674-5647.2016.01.07
UR - https://global-sci.org/intro/article_detail/cmr/18666.html
KW - meromorphic function, shared value, normal criterion.
AB - <p style="text-align: justify;">In this paper, we consider normality criteria for a family of meromorphic
functions concerning shared values. Let&nbsp;$\mathcal{F}$&nbsp;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, <strong>52</strong>:
241–289), Li and Gu (Li Y T, Gu Y X. On normal families of meromorphic functions. $J$. $Math$. $Anal$. $Appl$., 2009, <strong>354</strong>: 421–425).</p>