Periodic Points and Normality Concerning Meromorphic Functions with Multiplicity

doi:10.1007/s10473-020-0515-9

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	Periodic Points and Normality Concerning Meromorphic Functions with Multiplicity
	Deng, Bingmao 1; Fang, Mingliang 2; Wang, Yuefei3,4
	2020-09-01
发表期刊	ACTA MATHEMATICA SCIENTIA
ISSN	0252-9602
卷号	40 期号:5 页码:1429-1444
摘要	In this article, two results concerning the periodic points and normality of meromorphic functions are obtained: (i) the exact lower bound for the numbers of periodic points of rational functions with multiple fixed points and zeros is proven by lettingR(z) be a non-polynomial rational function, and if all zeros and poles ofR(z) -zare multiple, thenR(k)(z) has at leastk+ 1 fixed points in the complex plane for each integerk >= 2; (ii) a complete solution to the problem of normality of meromorphic functions with periodic points is given by letting F be a family of meromorphic functions in a domainD, and lettingk >= 2 be a positive integer. If, for eachf is an element of F, all zeros and poles off(z) -zare multiple, and its iterationf(k)has at mostkdistinct fixed points inD, then F is normal inD. Examples show that all of the conditions are the best possible.
关键词	normality iteration periodic points
DOI	10.1007/s10473-020-0515-9
收录类别	SCI
语种	英语
资助项目	NNSF of China[11688101]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000565212900015
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52091
专题	数学所
通讯作者	Fang, Mingliang
作者单位	1.Guangdong Univ Finance, Sch Financial Math & Stat, Guangzhou 510521, Peoples R China 2.Hangzhou Dianzi Univ, Dept Math, Hangzhou 310012, Peoples R China 3.Shenzhen Univ, Sch Math & Stat, Shenzhen 518060, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Deng, Bingmao,Fang, Mingliang,Wang, Yuefei. Periodic Points and Normality Concerning Meromorphic Functions with Multiplicity[J]. ACTA MATHEMATICA SCIENTIA,2020,40(5):1429-1444.
APA	Deng, Bingmao,Fang, Mingliang,&Wang, Yuefei.(2020).Periodic Points and Normality Concerning Meromorphic Functions with Multiplicity.ACTA MATHEMATICA SCIENTIA,40(5),1429-1444.
MLA	Deng, Bingmao,et al."Periodic Points and Normality Concerning Meromorphic Functions with Multiplicity".ACTA MATHEMATICA SCIENTIA 40.5(2020):1429-1444.