Abstract and Applied Analysis
Volume 2007 (2007), Article ID 60718, 6 pages
Research Article

Meromorphic Functions Sharing a Small Function

Songmin Wang and Zongsheng Gao

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.


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 n11 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.