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Research articles

ScienceAsia 47 (2021):ID 645-650 |doi: 10.2306/scienceasia1513-1874.2021.070


Normality of meromorphic functions and their differential polynomials


Jia Xiea, Yongyi Gub,*, Wenjun Yuanc,*

 
ABSTRACT:     In this paper, we study the normality of meromorphic families and prove the following theorem: Let k be a positive integer, P(z) be a non-constant polynomial satisfying P(0) = 0, h(≡ 0) be a holomorphic function in a domain D, H( f , f , . . . , f (k)) be a differential polynomial with Γγ |H < k + 1, and  be a meromorphic family in D. If, for each f ∈  , f = 0 and P( f (k)) + H( f , f , . . . , f (k)) = h for z ∈ D, then  is a normal family in D.

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a School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006 China
b Big data and Educational Statistics Application Laboratory, Guangdong University of Finance and Economics, Guangzhou 510320 China
c Department of Basic Courses Teaching, Software Engineering Institute of Guangzhou, Guangzhou 510990 China

* Corresponding author, E-mail: gdguyongyi@163.com, wjyuan1957@126.com

Received 24 Feb 2021, Accepted 4 Jun 2021