Abstract and Applied Analysis
Volume 2012 (2012), Article ID 582854, 11 pages
http://dx.doi.org/10.1155/2012/582854
Research Article

Normality Criteria of Meromorphic Functions That Share a Holomorphic Function

Jie Ding,1 Jianming Qi,2 and Taiying Zhu2

1School of Mathematics, Shandong University, Jinnan 250100, China
2Department of Mathematics and Physics, Shanghai Dianji University, Shanghai 201306, China

Received 11 October 2011; Accepted 29 November 2011

Academic Editor: Allan C Peterson

Copyright © 2012 Jie Ding 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

Let F be a family of meromorphic functions defined in D, let ψ(≢0), a0,a1,...,ak-1 be holomorphic functions in D, and let k be a positive integer. Suppose that, for every function f∈F, f≠0, P(f)=f(k)+ak-1f(k-1)+⋯+a1f'+a0f≠0 and, for every pair functions (f,g)∈F, P(f), P(g) share ψ, then F is normal in D.