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\(\ mathcal F \)和\(\ mathcal G \)是D上亚纯函数的两个族,其零是多个。假设\(\ mathcal G \)在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f和g共享0和\(\ infty \),而\(f'\)和\(g'\)共享1,则\(\ mathcal F \)在D上也是正常的。