On normal families and differential polynomials for meromorphic functions

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• 作者：Qian Lu
• 关键词：Differential polynomials ; Meromorphic functions ; Zeros ; Normality
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2008
• 出版时间：1 April 2008
• 年：2008
• 卷：340
• 期：1
• 页码：394-400
• 全文大小：125 K

文摘

We consider the normality criterion for a families meromorphic in the unit disc Δ, and show that if there exist functions a(z) holomorphic in Δ, a(z)≠1, for each 41a2e40a64da527ca5e54"" title=""Click to view the MathML source"">zΔ, such that there not only exists a positive number ε₀ such that |a_n(a(z)−1)−1|ε₀ for arbitrary sequence of integers and for any 1a2038114166d3a8cd2fd60c9bf0c"" title=""Click to view the MathML source"">zΔ, but also exists a positive number B>0 such that for every , B|f^′(z)||f(z)| whenever f(z)f^″(z)−a(z)(f^′(z))²=0 in Δ. Then is normal in Δ.