Normal families of meromorphic functions with multiple zeros and poles

2003 ◽  
Vol 136 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Xuecheng Pang ◽  
Lawrence Zalcman
Keyword(s):  
Meromorphic Functions ◽  
Normal Families ◽  
Multiple Zeros ◽  
Zeros And Poles

Exceptional functions and normal families of holomorphic functions with multiple zeros

2011 ◽  
Vol 18 (1) ◽  
pp. 31-38
Author(s):  
Jun-Fan Chen
Keyword(s):  
Positive Integer ◽  
Meromorphic Functions ◽  
Normal Family ◽  
Holomorphic Functions ◽  
Normal Families ◽  
Multiple Zeros ◽  
Zeros Of Functions

Abstract Let k be a positive integer, and let ℱ be a family of functions holomorphic on a domain D in C, all of whose zeros are of multiplicity at least k + 1. Let h be a function meromorphic on D, h ≢ 0, ∞. Suppose that for each ƒ ∈ ℱ, ƒ(k)(z) ≠ h(z) for z ∈ D. Then ℱ is a normal family on D. The condition that the zeros of functions in ℱ are of multiplicity at least k + 1 cannot be weakened, and the corresponding result for families of meromorphic functions is no longer true.

scholarly journals Exceptional functions and normal families of meromorphic functions with multiple zeros

2008 ◽  
Vol 341 (1) ◽  
pp. 224-234 ◽  
Author(s):  
Chunlin Lei ◽  
Mingliang Fang ◽  
Degui Yang ◽  
Xueqin Wang
Keyword(s):  
Meromorphic Functions ◽  
Normal Families ◽  
Multiple Zeros

scholarly journals Normal families and composite meromorphic functions

2011 ◽  
Vol 41 (11) ◽  
pp. 991-1000
Author(s):  
JianMing LIN ◽  
Bing XIAO ◽  
WenJun YUAN
Keyword(s):  
Meromorphic Functions ◽  
Normal Families

Normal Families of Meromorphic Functions whose Derivatives Omit a Function

2003 ◽  
Vol 2 (1) ◽  
pp. 257-265 ◽  
Author(s):  
Xuecheng Pang ◽  
Degui Yang ◽  
Lawrence Zalcman
Keyword(s):  
Meromorphic Functions ◽  
Normal Families
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