Journal of Applied Mathematics
Volume 2011 (2011), Article ID 790942, 9 pages
http://dx.doi.org/10.1155/2011/790942
Research Article

Normal Criteria of Function Families Concerning Shared Values

Wenjun Yuan,1 Bing Zhu,2 and Jianming Lin3

1School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
2College of Computer Engineering Technology, Guangdong Institute of Science and Technology, Zhuhai 519090, China
3School of Economic and Management, Guangzhou University of Chinese Medicine, Guangzhou 510006, China

Received 10 July 2011; Accepted 7 September 2011

Academic Editor: Hui-Shen Shen

Copyright © 2011 Wenjun Yuan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the normality of families of meromorphic functions concerning shared values. We consider whether a family of meromorphic functions ℱ is normal in 𝐷 , if, for every pair of functions 𝑓 and 𝑔 in ℱ, 𝑓 − 𝑎 𝑓 − 𝑛 and 𝑔 − 𝑎 𝑔 − 𝑛 share the value 𝑏 , where 𝑎 and 𝑏 are two finite complex numbers such that 𝑎 ≠ 0 , 𝑛 is a positive integer. Some examples show that the conditions in our results are best possible.