Normality and Quasinormality of Zero-free Meromorphic Functions

Let k, K ∈1N and F be a family of zero-free meromorphic functions in a domain D such that for each f ∈ F, f（k） - 1 has at most K zeros, ignoring multiplicity. Then F is quasinormal of order at most v=k/k＋1,where v is equal to the largest integer not exceeding k/k＋1.In particular, if K = k, then F is...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2012-04, Vol.28 (4), p.707-716
Main Author: Chang, Jian Ming
Format: Article
Language:English
Subjects:
Integers
Linear algebra
Linear equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Meromorphic functions
Normality
Numbers
Studies
亚纯函数
多样性
拟正规
整数
零点
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Summary:Let k, K ∈1N and F be a family of zero-free meromorphic functions in a domain D such that for each f ∈ F, f（k） - 1 has at most K zeros, ignoring multiplicity. Then F is quasinormal of order at most v=k/k＋1,where v is equal to the largest integer not exceeding k/k＋1.In particular, if K = k, then F is normal. The results are sharp.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-011-0297-z