2007Journal of Shanxi Normal UniversityRequires access

Normality and Shared Values

Zheng Li

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Abstract

In this paper,the authors draw a connection between normal family and sharing values.They obtain the following normal criterions:Let F be a family of meromorphic functions defined in a domain D,a,b∈c,a,b≠1,.If f∈F,f and f'share the value 1 in D,f=a ■ f'=b,then F is normal in D.Let F be a family of holomorphic functions defined in a domain D,k∈N+,b∈R+,.If f∈F,the zeros f-1 are of multiplicity ≥k,f=1 ■ f(k)=1,f(k)=1 ■ 0|f(k+1)|≤b,Then F is normal in D.

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What this paper is about

In this paper,the authors draw a connection between normal family and sharing values.They obtain the following normal criterions:Let F be a family of meromorphic functions defined in a domain D,a,b∈c,a,b≠1,.If f∈F,f and f'share the value 1 in D,f=a ■ f'=b,then F is normal in D.Let F be a family of holomorphic functions defined in a domain D,k∈N+,b∈R+,.If f∈F,the zeros f-1 are of multiplicity ≥k,f=1 ■ f(k)=1,f(k)=1 ■ 0|f(k+1)|≤b,Then F is normal in D.

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Available abstract

In this paper,the authors draw a connection between normal family and sharing values.They obtain the following normal criterions:Let F be a family of meromorphic functions defined in a domain D,a,b∈c,a,b≠1,.If f∈F,f and f'share the value 1 in D,f=a ■ f'=b,then F is normal in D.Let F be a family of holomorphic functions defined in a domain D,k∈N+,b∈R+,.If f∈F,the zeros f-1 are of multiplicity ≥k,f=1 ■ f(k)=1,f(k)=1 ■ 0|f(k+1)|≤b,Then F is normal in D.

Key concepts: Meromorphic function, Normal family, Holomorphic function, Normality, Multiplicity (mathematics), Mathematics, Combinatorics, Domain (mathematical analysis)

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