Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-30T19:39:18.289Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected], [email protected])
Fengqin Wu
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210097, People's Republic of China ([email protected], [email protected])
Liangwen Liao
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China ([email protected])
Get access Rights & Permissions [Opens in a new window]

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)