Research articles
ScienceAsia 46 (2020): 227234 doi:
10.2306/scienceasia15131874.2020.027
Normal families of meromorphic functions which share
a set
Jinhua Cai, Fanning Meng, Jia Xie, Wenjun Yuan^{*}
ABSTRACT: In this paper, by using the Nevanlinna’s value distribution theory and the method of ZalcmanPang, it investigates the normality of a family of meromorphic functions, denoted by , defined in a domain D, which concerns
the conditions for each ƒ ∈ : (i) E(S_{1}, ƒ ) = E (S_{2}, ( ƒ (k))q); (ii) both zeros and poles of ƒ −a have multiplicities at least k (> 2 or 2) and k + 1, respectively, or k ( 4) and k − 1, respectively, where k and q are positive integers, a is any finite complex number, S_{1} = {a_{1}, a_{2}, a_{3}} and S_{2 }= {b_{1}, b_{2}, b_{3}} are made up of finite complex numbers. The conclusion still holds if condition (ii) is replaced by the assumption that zeros of ƒ − a_{i }have multiplicities at least k, where k 1 and i = 1, 2, 3.
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^{a} 
School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006 China 
* Corresponding author, Email: wjyuan1957@126.com
Received 8 Jul 2019, Accepted 9 Apr 2020
