Computational Methods and Function Theory 2 (2002), No. 1, 257--265
Copyright Heldermann Verlag 2002
Xuecheng Pang
xcpang@euler.math.ecnu.edu.cn, Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China.
Degui Yang
dyang@scau.edu.cn, College of Sciences, South China Agricultural University, Guangzhou 510642, P. R. China.
Lawrence Zalcman
zalcman@macs.biu.ac.il, Department of Mathematics and Statistics, Bar-Ilan University, 52900 Ramat-Gan, Israel.
Let $\mathcal{F}$ be a family of functions meromorphic on the plane domain~$D$, and let $h$ be a holomorphic function on $D$, $h\not\equiv0$. Suppose that, for each $f\in\mathcal{F}$, $f^{(m)}(z)\not=h(z) $ for $z\in D$. Then $\mathcal{F}$ is normal on $D$ (i) if all zeros of functions in $\mathcal{F}$ have multiplicity at least $m+3$, or (ii) if all zeros of functions in $\mathcal{F}$ have multiplicity at least $m+2$ and $h$ has only multiple zeros on $D$, or (iii) if all poles of functions in $\mathcal{F}$ are multiple and all zeros have multiplicity at least $m+2$.
Keywords: Normal families, omitted functions.
MSC 2000: 30D45.
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