Some normality criteria for families of meromorphic functions

Wenjun Yuan,Weiling Xiong,Jianming Lin

doi:10.1186/1029-242x-2013-459

Abstract

Abstract In the note, we study the normality of families of meromorphic functions. We consider whether a family of meromorphic functions ℱ is normal in D if, for a normal family G and for each function f ∈ F , there exists g ∈ G such that f n f ′ = a i implies g n g ′ = a i for two distinct nonzero points a i , i = 1 , 2 and an integer n. An example shows that the condition in our results is best possible. MSC:30D45, 30D35.

Highlights

Introduction and main resultsLet f (z) and g(z) be two nonconstant meromorphic functions in a domain D ⊆ C, and let a be a finite complex value
The principle is false in general, many authors proved normality criterion for families of meromorphic functions corresponding to a LiouvillePicard type theorem
Let F be a family of meromorphic functions on D and n ∈ N

Summary

Introduction

Introduction and main resultsLet f (z) and g(z) be two nonconstant meromorphic functions in a domain D ⊆ C, and let a be a finite complex value. The principle is false in general (see [ ]), many authors proved normality criterion for families of meromorphic functions corresponding to a LiouvillePicard type theorem (see [ ]).

Results

Conclusion