Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Picard values and normal families of meromorphic functions

Yan Xua1, Fengqin Wua1 and Liangwen Liaoa2

a1 Department of Mathematics, Nanjing Normal University, Nanjing 210097, People's Republic of China (xuyan@njnu.edu.cn, wufengqin0635@126.com)

a2 Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China (maliao@nju.edu.cn)

Abstract

Let f be a transcendental meromorphic function on the complex plane xs2102, let a be a non-zero finite complex number and let n and k be two positive integers. In this paper, we prove that if nk+1, then $\smash{f+a(f^{(k)})^n}$ assumes each value bxs2208xs2102 infinitely often. Also, the related normal criterion for families of meromorphic functions is given. Our results generalize the related results of Fang and Zalcman.

(Received May 27 2008)

(Accepted November 05 2008)