Normality and Shared Values
Zheng Li
Abstract
Zheng Li
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.
A significance statement is not available in the OpenAlex record.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
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)