Q α-Normal Families and Entire Functions

2012 ◽  
Vol 12 (2) ◽  
pp. 597-651
Author(s):  
Shai Gul ◽  
Shahar Nevo
Keyword(s):  
Entire Functions ◽  
Normal Families

scholarly journals Uniqueness theorems and normal families of entire functions and their derivatives

2009 ◽  
Vol 95 (1) ◽  
pp. 67-75 ◽  
Author(s):  
Feng Lü ◽  
Junfeng Xu ◽  
Hongxun Yi
Keyword(s):  
Entire Functions ◽  
Normal Families ◽  
Uniqueness Theorems

scholarly journals Entire functions sharing a polynomial with their derivatives and normal families

Analysis ◽  
2008 ◽  
Vol 28 (1) ◽  
Author(s):  
Jürgen Grahl ◽  
Chao Meng
Keyword(s):  
Entire Functions ◽  
Normal Families

Letis constant. Furthermore, we prove the corresponding normality criterion.

scholarly journals Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives

2009 ◽  
Vol 2009 ◽  
pp. 1-9
Author(s):  
Jianming Qi ◽  
Feng Lü ◽  
Ang Chen
Keyword(s):  
Entire Function ◽  
Nonnegative Integer ◽  
Entire Functions ◽  
Normal Families ◽  
Transcendental Entire Function ◽  
Complex Numbers

We use the theory of normal families to prove the following. LetQ1(z)=a1zp+a1,p−1zp−1+⋯+a1,0andQ2(z)=a2zp+a2,p−1zp−1+⋯+a2,0be two polynomials such thatdeg⁡Q1=deg⁡Q2=p(wherepis a nonnegative integer) anda1,a2(a2≠0)are two distinct complex numbers. Letf(z)be a transcendental entire function. Iff(z)andf′(z)share the polynomialQ1(z) CMand iff(z)=Q2(z)wheneverf′(z)=Q2(z), thenf≡f′. This result improves a result due to Li and Yi.

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