Normality Criteria of Zero-free Meromorphic Functions

XIE JIE, DENG Bing-mao

doi:10.13371/j.cnki.chin.q.j.m.2019.03.001

Chinese Quarterly Journal of Mathematics >

2019 , Vol. 34 >Issue 3: 221 - 231

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2019.03.001

Normality Criteria of Zero-free Meromorphic Functions

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School of Mathematics and Information Science, Guangzhou University School of Financial Mathematics and Statistics, Guangdong University of Finance

Received date: 2016-12-19

Online published: 2020-08-22

Supported by

Supported by the NNSF of China(No.11701188)

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Abstract

Let k be a positive integer,let h（z）■0 be a holomorphic functions in a domain D,and let F be a family of zero-free meromorphic functions in D,all of whose poles have order at least l.If,for each f∈P（f）（z）-h（z） has at most k+l-1 distinct zeros（ignoring multiplicity） in D,where P（f）（z）=f^（k）（z）+a₁（z）f⁽（k-1）（z）+…+ak（z）f（z） is a differential polynomial of f and aj（z）（j=1,2,···,k） are holomorphic functions in D,then F is normal in D.

Key words： Meromorphic Functions; Normality; Zero-free

Cite this article

XIE JIE, DENG Bing-mao . Normality Criteria of Zero-free Meromorphic Functions[J]. Chinese Quarterly Journal of Mathematics, 2019 , 34(3) : 221 -231 . DOI: 10.13371/j.cnki.chin.q.j.m.2019.03.001

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