Abstract and Applied Analysis
Volume 2010 (2010), Article ID 147878, 14 pages
doi:10.1155/2010/147878
Research Article

Some Normal Criteria about Shared Values with Their Multiplicity Zeros

Jianming Qi and Taiying Zhu

Department of Mathematics and Physics, Shanghai Dianji University, Shanghai 200240, China

Received 8 March 2010; Revised 4 December 2010; Accepted 20 December 2010

Academic Editor: Ülle Kotta

Copyright © 2010 Jianming Qi and Taiying Zhu. 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

Let ℱ be a family of meromorphic functions in the domain 𝐷 , all of whose zeros are multiple. Let 𝑛 ( 𝑛 ≥ 2 ) be an integer and let 𝑎 , 𝑏 be two nonzero finite complex numbers. If 𝑓 + 𝑎 ( 𝑓 ) 𝑛 and 𝑔 + 𝑎 ( 𝑔 ) 𝑛 share 𝑏 in 𝐷 for every pair of functions 𝑓 , 𝑔 ∈ ℱ , then ℱ is normal in 𝐷 .