Normality Criteria of Meromorphic Functions That Share a Holomorphic Function

Let ℱ be a family of meromorphic functions defined in D, let ψ(≢0), a0,a1,...,ak-1 be holomorphic functions in D, and let k be a positive integer. Suppose that, for every function f∈ℱ, f≠0, P(f)=f(k)+ak-1f(k-1)+⋯+a1f′+a0f≠0 and, for every pair functions (f,g)∈ℱ, P(f), P(g) share ψ, then ℱ is normal...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2012-01, Vol.2012 (1), p.753-763-446
Main Authors: Ding, Jie, Qi, Jianming, Zhu, Taiying
Format: Article
Language:English
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Summary:Let ℱ be a family of meromorphic functions defined in D, let ψ(≢0), a0,a1,...,ak-1 be holomorphic functions in D, and let k be a positive integer. Suppose that, for every function f∈ℱ, f≠0, P(f)=f(k)+ak-1f(k-1)+⋯+a1f′+a0f≠0 and, for every pair functions (f,g)∈ℱ, P(f), P(g) share ψ, then ℱ is normal in D.
ISSN:1085-3375
1687-0409
DOI:10.1155/2012/582854