Normal Families and Shared Values of Meromorphic Functions
Zhang He-qiong
Abstract
Zhang He-qiong
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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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