periodicpointsandnormalfamiliesconcerningmultiplicity

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	periodicpointsandnormalfamiliesconcerningmultiplicity
	Deng Bingmao 1; Fang Mingliang 1; Wang Yuefei2
	2019-01-01
发表期刊	sciencechinamathematics
ISSN	1674-7283
卷号	62 期号:3 页码:535
摘要	In 1992, Yang Lo posed the following problem: let F be a family of entire functions, let D be a domain in C, and let k 2 be a positive integer. If, for every f F, both f and its iteration f(k) have no fixed points in D, is F normal in D? This problem was solved by Essen and Wu in 1998, and then solved for meromorphic functions by Chang and Fang in 2005. In this paper, we study the problem in which f and f(k) have fixed points. We give positive answers for holomorphic and meromorphic functions.Let F be a family of holomorphic functions in a domain D and let k 2 be a positive integer. If, for each f F, all zeros of f(z) - z are multiple and f(k) has at most k distinct fixed points in D, then F is normal in D. Examples show that the conditions all zeros of f(z) - z are multiple and f(k) having at most k distinct fixed points in D are the best possible.Let F be a family of meromorphic functions in a domain D, and let k 2; l be two positive integers satisfying l 4 for k = 2 and l 3 for k 3. If, for each f F, all zeros of f(z) - z have a multiplicity at least l and f(k) has at most one fixed point in D, then F is normal in D. Examples show that the conditions l 3 for k 3 and f(k) having at most one fixed point in D are the best possible.
语种	英语
资助项目	[National Natural Science Foundation of China] ; [Graduate Student Overseas Study Program from South China Agricultural University]
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/39233
专题	数学所
作者单位	1.华南农业大学 2.中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Deng Bingmao,Fang Mingliang,Wang Yuefei. periodicpointsandnormalfamiliesconcerningmultiplicity[J]. sciencechinamathematics,2019,62(3):535.
APA	Deng Bingmao,Fang Mingliang,&Wang Yuefei.(2019).periodicpointsandnormalfamiliesconcerningmultiplicity.sciencechinamathematics,62(3),535.
MLA	Deng Bingmao,et al."periodicpointsandnormalfamiliesconcerningmultiplicity".sciencechinamathematics 62.3(2019):535.