论文标题
通过共享具有衍生物的功能对通过的正态性
Normality through sharing of pairs of functions with derivatives
论文作者
论文摘要
令$ \ Mathcal {F} \ subset \ Mathcal {M}（D）$，让$ A，B $和$ C $为三个不同的复数数字。如果在$ d $上存在$ h $和正常$ρ$，以使得每个$ f \ in \ mathcal {f}，$ $ f $ and $ $ f $和$ f^{'} $部分共享三对函数$（a，a，h），\（b，c_f）$和$ d_ $ d_ $ d_ $ d_ $ c，d_ $ d_ $ c，c，d_ $ d_ $ d_ $ c，d _穿刺磁盘$ d^*_ρ（0），然后$ \ mathcal {f} $在$ d $中是正常的。这是Schwick结果的改进[Arch。数学。 （巴塞尔），\ textbf {59}（1992），50-54]。我们还获得了几个正态性标准，这些标准可显着改善现有结果，并提供示例以建立结果的清晰度。
Let $\mathcal{F}\subset\mathcal{M}(D)$ and let $a, b$ and $c$ be three distinct complex numbers. If, there exist a holomorphic function $h$ on $D$ and a positive constant $ρ$ such that for each $f\in\mathcal{F},$ $f$ and $f^{'}$ partially share three pairs of functions $(a,h), \ (b, c_f)$ and $(c,d_f)$ on $D,$ where $c_f$ and $d_f$ are some values in some punctured disk $D^*_ρ(0),$ then $\mathcal{F}$ is normal in $D$. This is an improvement of Schwick's result[Arch. Math. (Basel), \textbf{59} (1992), 50-54]. We also obtain several normality criteria which significantly improve the existing results and examples are given to establish the sharpness of results.
