Abstract and Applied Analysis
Volume 2007 (2007), Article ID 60718, 6 pages
doi:10.1155/2007/60718
Research Article
Meromorphic Functions Sharing a Small Function
LMIB and Department of Mathematics, Beihang University, Beijing 100083, China
Received 25 September 2006; Revised 18 January 2007; Accepted 26 March 2007
Academic Editor: Y. Giga
Copyright © 2007 Songmin Wang and Zongsheng Gao. 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 will study meromorphic functions that share a small function, and prove the following result: let f(z) and g(z) be two transcendental meromorphic functions in the complex plane and let n≥11 be a positive integer. Assume that a(z)(≢0) is a common small function with respect to f(z) and g(z). If fnf′ and gng′ share a(z) CM, then either fn(z)f′(z)gn(z)g′(z)≡a2(z), or f(z)≡tg(z) for a constant satisfying tn+1=1. As applications, we give several examples.