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Picard values and normal families of meromorphic functions

Published online by Cambridge University Press:  21 September 2009

Yan Xu ,
Fengqin Wu  and
Liangwen Liao
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)
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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 n≥k+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.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 5 , October 2009 , pp. 1091 - 1099
Copyright
Copyright © Royal Society of Edinburgh 2009

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