2007Journal of Jiangxi Normal UniversityRequires access

Shared Values and Normal Families

Lipei Liu

Open publisher page 5 citations

Abstract

In this paper the problem of normal families of meromorphic with relation to shared values has been researched,and the following result is proved:let F be a family of meromorphic functions in D,and a,b,c,d be four distinct finite complex values such that b≠0,c≠a and d≠b,and k be a positive integer.If for every f∈F,the zeros of f-c are multiplicity ≥k and f(z)=af(k)(z)=b,f(z)=c■f(k)(z)=d,then F is normal in D.This resut extends the normality criterion of Chang Jianming.

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What this paper is about

In this paper the problem of normal families of meromorphic with relation to shared values has been researched,and the following result is proved:let F be a family of meromorphic functions in D,and a,b,c,d be four distinct finite complex values such that b≠0,c≠a and d≠b,and k be a positive integer.If for every f∈F,the zeros of f-c are multiplicity ≥k and f(z)=af(k)(z)=b,f(z)=c■f(k)(z)=d,then F is normal in D.This resut extends the normality criterion of Chang Jianming.

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Available abstract

In this paper the problem of normal families of meromorphic with relation to shared values has been researched,and the following result is proved:let F be a family of meromorphic functions in D,and a,b,c,d be four distinct finite complex values such that b≠0,c≠a and d≠b,and k be a positive integer.If for every f∈F,the zeros of f-c are multiplicity ≥k and f(z)=af(k)(z)=b,f(z)=c■f(k)(z)=d,then F is normal in D.This resut extends the normality criterion of Chang Jianming.

Key concepts: Meromorphic function, Normal family, Normality, Multiplicity (mathematics), Mathematics, Combinatorics, Integer (computer science), Pure mathematics

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