## Journal of Applied Mathematics

### Normal Criterion Concerning Shared Values

#### Abstract

We study normal criterion of meromorphic functions shared values, we obtain the following. Let $F$ be a family of meromorphic functions in a domain $D$, such that function $f\in F$ has zeros of multiplicity at least 2, there exists nonzero complex numbers ${b}_{f},{c}_{f}$ depending on $f$ satisfying $(\text{i}) {b}_{f}/{c}_{f}$ is a constant;  $(\text{i}\text{i})\mathrm{min} \{\sigma (0,{b}_{f}),\sigma (0,{c}_{f}),\sigma ({b}_{f},{c}_{f})\ge m\}$ for some $m>0$;  $(\text{i}\text{i}\text{i}) (1/{c}_{f}^{k-1})({f}^{\prime }{)}^{k}(z)+f(z)\ne {b}_{f}^{k}/{c}_{f}^{k-1}$ or $(1/{c}_{f}^{k-1})({f}^{\prime }{)}^{k}(z)+f(z)={b}_{f}^{k}/{c}_{f}^{k-1}{\Rightarrow}f(z)={b}_{f}$, then $F$ is normal. These results improve some earlier previous results.

#### Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 312324, 7 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.jam/1355495289

Digital Object Identifier
doi:10.1155/2012/312324

Mathematical Reviews number (MathSciNet)
MR2970426

Zentralblatt MATH identifier
1253.30046

#### Citation

Chen, Wei; Zhang, Yingying; Zeng, Jiwen; Tian, Honggen. Normal Criterion Concerning Shared Values. J. Appl. Math. 2012 (2012), Article ID 312324, 7 pages. doi:10.1155/2012/312324. https://projecteuclid.org/euclid.jam/1355495289