Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 908123, 12 pages
http://dx.doi.org/10.1155/2012/908123
Research Article

Normal Families of Zero-Free Meromorphic Functions

Department of Basic Courses, Shaanxi Railway Institute, Weinan 714000, Shaanxi, China

Received 26 March 2012; Accepted 7 August 2012

Academic Editor: Sergey V. Zelik

Copyright © 2012 Yuntong Li. 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.

Abstract

Let 𝑎 ( 0 ) , 𝑏 , and 𝑛 and 𝑘 be two positive integers such that 𝑛 2 . Let be a family of zero-free meromorphic functions defined in a domain 𝒟 such that for each 𝑓 , 𝑓 + 𝑎 ( 𝑓 ( 𝑘 ) ) 𝑛 𝑏 has at most 𝑛 𝑘 zeros, ignoring multiplicity. Then is normal in 𝒟 .