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Normality Concerning Shared Values Between two Families
Computational Methods and Function Theory ( IF 0.6 ) Pub Date : 2021-05-04 , DOI: 10.1007/s40315-021-00376-7
Jianming Chang

We improve a normality result of Liu–Li–Pang [4] concerning shared values between two families. Let \(\mathcal F\) and \(\mathcal G\) be two families of meromorphic functions on D whose zeros are multiple. Suppose that \(\mathcal G\) is normal on D, and no sequence contained in \(\mathcal G\) \(\chi \)-converges locally uniformly to \(\infty \) or a function g satisfying \(g'\equiv 1\). If for every \(f\in \mathcal F\), there exists a function \(g\in \mathcal G\) such that f and g share 0 and \(\infty \) while \(f'\) and \(g'\) share 1, then \(\mathcal F\) is also normal on D.



中文翻译:

关于两个家庭之间的共同价值的常态性

关于两个家庭之间的共同价值观,我们改善了刘立鹏[4]的正态性结果。令\(\ mathcal F \)\(\ mathcal G \)D上亚纯函数的两个族,其零是多个。假设\(\ mathcal G \)D上是正常的,并且\(\ mathcal G \) \(\ chi \)中不包含任何序列-局部均匀收敛于\(\ infty \)或满足g (\ g'\ equiv 1 \)。如果对于每个\(f \ in \ mathcal F \),存在一个函数\(g \ in \ mathcal G \)这样fg共享0和\(\ infty \),\(f'\)\(g'\)共享1,则\(\ mathcal F \)D上也是正常的。

更新日期:2021-05-05
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