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Picard values and normal families of meromorphic functions

Published online by Cambridge University Press:  21 September 2009

Yan Xu
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210097, People's Republic of China (xuyan@njnu.edu.cn, wufengqin0635@126.com)
Fengqin Wu
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210097, People's Republic of China (xuyan@njnu.edu.cn, wufengqin0635@126.com)
Liangwen Liao
Affiliation:
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 ℂ, 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 assumes each value b∈ℂ infinitely often. Also, the related normal criterion for families of meromorphic functions is given. Our results generalize the related results of Fang and Zalcman.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2009

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