Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 826164, 6 pages
http://dx.doi.org/10.1155/2011/826164
Research Article

Normal Criteria of Function Families Related to a Result of Drasin

Zhu Bing,1 Lin Jianming,2 and Yuan Wenjun3

1College of Computer Engineering Technology, Guangdong Institute of Science and Technology, Zhuhai 519090, China
2School of Economic and Management, Guangzhou University of Chinese Medicine, Guangzhou 512009, China
3School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

Received 7 April 2011; Accepted 20 May 2011

Academic Editor: M. De la Sen

Copyright © 2011 Zhu Bing 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 related to a result of Drasin. We consider whether a family meromorphic functions ℱ whose each function does not take zero is normal in 𝐷 , if for every pair of functions 𝑓 and 𝑔 in ℱ , 𝑓 ( 𝑧 ) and 𝑔 ( 𝑧 ) share ∞ or 𝐻 ( 𝑓 ) − 1 and 𝐻 ( 𝑔 ) − 1 share 0, where 𝐻 ( 𝑓 ) ∶ = 𝑓 ( 𝑘 ) ( 𝑧 ) + 𝑎 𝑘 − 1 𝑓 ( 𝑘 − 1 ) ( 𝑧 ) + ⋯ , 𝑎 0 𝑓 ( 𝑧 ) . Some examples show that the conditions in our results are best possible.