## Abstract and Applied Analysis

### Normality Criteria of Meromorphic Functions That Share a Holomorphic Function

#### Abstract

Let $\mathcal{F}$ be a family of meromorphic functions defined in $D$, let $\psi (\cancel{\not\equiv }0)$, ${a}_{0},{a}_{1},...,{a}_{k-1}$ be holomorphic functions in $D$, and let $k$ be a positive integer. Suppose that, for every function $f\in \mathcal{F}$, $f\ne 0$, $P(f)={f}^{(k)}+{a}_{k-1}{f}^{(k-1)}+\cdots +{a}_{1}f\text{'}+{a}_{0}f\ne 0$ and, for every pair functions $(f,g)\in \mathcal{F}$, $P(f)$, $P(g)$ share $\psi$, then $\mathcal{F}$ is normal in $D$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 582854, 11 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.aaa/1355495628

Digital Object Identifier
doi:10.1155/2012/582854

Mathematical Reviews number (MathSciNet)
MR2872318

Zentralblatt MATH identifier
1239.30020

#### Citation

Ding, Jie; Qi, Jianming; Zhu, Taiying. Normality Criteria of Meromorphic Functions That Share a Holomorphic Function. Abstr. Appl. Anal. 2012 (2012), Article ID 582854, 11 pages. doi:10.1155/2012/582854. https://projecteuclid.org/euclid.aaa/1355495628

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