Normal Families of Meromorphic Functions and Shared Set

doi:10.13371/j.cnki.chin.q.j.m.2015.02.001

Chinese Quarterly Journal of Mathematics ›› 2015, Vol. 30 ›› Issue (2): 159-165.doi: 10.13371/j.cnki.chin.q.j.m.2015.02.001

1. School of Mathematics Science, Xinjiang Normal University 2. School of Mathematics and Information Science, Guangzhou University

Received:2013-03-19 Online:2015-06-30 Published:2020-11-23
About author:TIAN Hong-gen(1957-), male, native of Hanjiang, Jiangsu, a professor of Xinjiang Normal University, engages in complex analysis; CHEN Wei(1988-), male, native of Ruichang, Jiangxi, a student of Xinjiang Normal University, M.S.D., engages in complex analysis and its applications; YUAN Wen-jun(1957-), male, native of Anyue, Sichuan, a professor of Guangzhou University, Ph.D., engages in complex analysis and its applications.
Supported by:
Supported by the National Natural Science Foundation of China(11461070,11271090)； Supported by the Natural Science Foundation of Guangdong Province(S2012010010121)；

Abstract

Abstract: In this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f have multiplicity at least 2 and there exist nonzero complex numbers bf,c_fsatisfying（i） b_f/c_fis a constant;（ii） min{σ（0,b_f）,σ（0,c_f）,σ（b_f,c_f）} ≥m for some m > 0;（iii） E_f’（S_f）\subseteq E_f（S_f）,where S_f = {b_f,c_f}.Then F is normal in A.At the same time,the corresponding results are also proved.The results in this paper improve and generalize the related results of[10-11]and[7].

Key words: meromorphic function, shared set, normal family

CLC Number:

O174.52

TIAN Hong-gen, CHEN Wei, YUAN Wen-jun. Normal Families of Meromorphic Functions and Shared Set[J]. Chinese Quarterly Journal of Mathematics, 2015, 30(2): 159-165.

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[2]	YANG Qi, YUAN Wen-jun, TIAN Hong-gen. The Normal Family of Meromorphic Functions Concerning Shared Analytic Function [J]. Chinese Quarterly Journal of Mathematics, 2022, 37(1): 26-36.
[3]	XIE JIE, DENG Bing-mao. Normality Criteria of Zero-free Meromorphic Functions [J]. Chinese Quarterly Journal of Mathematics, 2019, 34(3): 221-231.
[4]	ZHANG Shui-ying, LIU Hui-fang. On Uniqueness Problem of Meromorphic Functins Sharing Values with Their q-shifts [J]. Chinese Quarterly Journal of Mathematics, 2019, 34(3): 232-241.
[5]	WANG Xue-qin, LEI Chun-lin. Normal Families and Shared Functions [J]. Chinese Quarterly Journal of Mathematics, 2015, 30(2): 267-273.
[6]	YANG Qi. Normality Criteria of Meromorphic Functions Concerning Shared Fixed-points [J]. Chinese Quarterly Journal of Mathematics, 2015, 30(1): 20-29.
[7]	DENG Bing-mao, LIU Dan, WANG Xue-qin, YANG De-gui. Normal Families of Zero-free Meromorphic Functions II [J]. Chinese Quarterly Journal of Mathematics, 2014, 29(3): 438-446.
[8]	LIU Dan, DENG Bing-mao, YANG De-gui. Normal Families of Zero-free Meromorphic Functions [J]. Chinese Quarterly Journal of Mathematics, 2013, 28(3): 402-407.
[9]	DENG Bing-mao, LEI Chun-lin, YANG De-gui. Normality and Shared Value Concerning Differential Polynomials [J]. Chinese Quarterly Journal of Mathematics, 2013, 28(1): 87-92.
[10]	XIAO Bing, WU Qi-feng, YUAN Wen-jun. A Note on Normal Families of Meromorphic Functions and Sharing Set [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(3): 360-365.
[11]	LIU Zhi-hong, LI Ying-chun, HUANG Bin. Normal Families of Holomorphic Functions Concerning Shared a Polynomial [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(3): 394-399.
[12]	QIU Hui-ling. Further Results of Meromorphic Functions that Share a Polynomial [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(3): 448-452.
[13]	SU Xian-feng, GAO Ling-yun. On the Order of the Solutions of Systems of Complex Algebraic Diﬀerential Equations [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(2): 196-199.
[14]	ZHANG Ji-long. Meromorphic Functions That Share Two Sets [J]. Chinese Quarterly Journal of Mathematics, 2010, 25(4): 530-534.
[15]	XIONG Wei-ling. Uniqueness of Entire Functions Concerning Differential Polynomials [J]. Chinese Quarterly Journal of Mathematics, 2010, 25(2): 214-219.

Normal Families of Meromorphic Functions and Shared Set

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