2009Journal of Southwest China Normal UniversityRequires access

Normal Families and Shared Values of Meromorphic Functions

Zhang He-qiong

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Abstract

In this paper,the author combines shared values of meromorphic functions with spherical derivative extended and proves the following theorem: Let F be a family of meromorphic functions in an area D,all of whose zeros are of multiplicity at least k,k is a positive integer number.If f∈F,f=0 if and only if f(k)=0,and suppose that there exists a positive integer M(1) such that |f(k)(z)|1+|f(z)|k+1≤M whenever z∈E-(1,f(k)),then F is normal.

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What this paper is about

In this paper,the author combines shared values of meromorphic functions with spherical derivative extended and proves the following theorem: Let F be a family of meromorphic functions in an area D,all of whose zeros are of multiplicity at least k,k is a positive integer number.If f∈F,f=0 if and only if f(k)=0,and suppose that there exists a positive integer M(1) such that |f(k)(z)|1+|f(z)|k+1≤M whenever z∈E-(1,f(k)),then F is normal.

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Available abstract

In this paper,the author combines shared values of meromorphic functions with spherical derivative extended and proves the following theorem: Let F be a family of meromorphic functions in an area D,all of whose zeros are of multiplicity at least k,k is a positive integer number.If f∈F,f=0 if and only if f(k)=0,and suppose that there exists a positive integer M(1) such that |f(k)(z)|1+|f(z)|k+1≤M whenever z∈E-(1,f(k)),then F is normal.

Key concepts: Meromorphic function, Multiplicity (mathematics), Normal family, Mathematics, Integer (computer science), Combinatorics, Derivative (finance), Discrete mathematics

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