Shared Values and Normal Families
Lipei Liu
Abstract
Lipei Liu
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)=af(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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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)=af(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