Let $k$ be a positive integer, and $m$ be an even number. Suppose that $a(z)(otequiv 0)$ is a holomorphic function with zeros of multiplicity $m$ in a domain $D$. Let $cal F$ be a family of meromorphic functions in a domain $D$ such that each $fincal F$ have zeros of multiplicity at least $k+1+m$ and poles of multiplicity at least $m+1$. It is mainly proved that for each pair $(f,g)incal F$, if $ff^{(k)}$ and $gg^{(k)}$ share $a(z)$ IM, then $cal F$ is normal in $D$. This result improves Hu and Meng's results published in Journal of Mathematical Analysis and Applications (2009, 2011), and also Jiang and Gao's result in Acta Matematica Scientia (2012).
展开▼
机译：假设$ k $为正整数，$ m $为偶数。假设$ a（z）（ not equiv 0）$是一个全纯函数，在域$ D $中具有零的多重性$ m $。假设$ cal F $是域$ D $中的亚纯函数族，使得每个$ f in cal F $的零点复数至少为$ k + 1 + m $，且极点的复数至少为$ m。 + 1 $。主要证明，对于每对$（f，g） in cal F $，如果$ ff ^ {（k）} $和$ gg ^ {（k）} $共享$ a（z）$ IM，那么$ cal F $在$ D $中是正常的。这个结果改进了胡和孟发表在《数学分析与应用学报》（2009，2011）上的结果，也改进了姜和高发表在《科学学报》（2012）上的结果。
展开▼
