A Note on Normal Families of Meromorphic Functions Concerning Shared Values

A Note on Normal Families of Meromorphic Functions Concerning Shared Values

We study the normality of families of meromorphic functions related to a Hayman conjecture. We consider whether a family of meromorphic functions ℱ is normal in D if, for every pair of functions f and g in ℱ, f′−afn and g′−agn share the value b for n=1,2, and 3, where a and b≠0 are two finite comple...

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Veröffentlicht in:Discrete Dynamics in Nature and Society 2011-01, Vol.2011 (1), p.617-626
Hauptverfasser: Wenjun, Yuan, Jinjin, Wei, Jianming, Lin
Format: Artikel
Sprache:eng
Schlagworte:
Functional equations
Functions
Mathematical analysis
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Zusammenfassung:We study the normality of families of meromorphic functions related to a Hayman conjecture. We consider whether a family of meromorphic functions ℱ is normal in D if, for every pair of functions f and g in ℱ, f′−afn and g′−agn share the value b for n=1,2, and 3, where a and b≠0 are two finite complex numbers. Some examples show that the conditions in our results are the best possible.
ISSN:1026-0226
1607-887X
DOI:10.1155/2011/463287