Bulletin

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Volume 35 • Number 2 • 2012

• Normality Criteria for Families of Meromorphic Function Concerning Shared Values
Jianming Qi, Jie Ding and Lianzhong Yang

Abstract.
Let

$k$ be a positive integer and let

$\mathcal{F}$ be a family of meromorphic functions in the plane domain

$D$ all of whose zeros with multiplicity at least

$k$ . Let

$P=a_pz^p+\cdots+a_2z^2+z$ be a polynomial,

$a_p,a_2\neq0$ and

$p=\deg(P)\geq k+2$ . If, for each

$f,g\in \mathcal{F}$ ,

$P(f)G(f)$ and

$P(g)G(g)$ share a non-zero constant

$b$ in

$D$ , where

$G(f)=f^{(k)}+H(f)$ be a differential polynomial of

$f$ satisfying

$\frac{w}{\deg}|_H\leq \frac{k}{l+1}+1$ or

$w(H)-\deg(H)<k$ , then

$\mathcal{F}$ is normal in

$D$ .

2010 Mathematics Subject Classification: 30D35, 30D45.

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