Computational Methods and Function Theory 2 (2002), No. 2, 385--395
Copyright Heldermann Verlag 2002
Mingliang Fang
mlfang@pine.njnu.edu.cn, Department of Mathematics, Nanjing Normal University, Nanjing 210097, P. R. China.
Lawrence Zalcman
zalcman@macs.biu.ac.il, Department of Mathematics and Statistics, Bar-Ilan University, 52900 Ramat-Gan, Israel.
This paper continues our investigation of conditions involving values shared by a function and its derivatives which imply the normality of families of meromorphic functions. In particular, we prove that if $\mathcal{F}$ is a family of meromorphic functions on the plane domain $D$, all of whose zeros have multiplicity at least $k+1$, and if $f(z)=a\Longleftrightarrow f^{(k)}(z)=b$ for all $f\in\mathcal{F}$ and $z\in D$ (where $a$ and $b$ are nonzero complex numbers), then $\mathcal{F}$ is normal on $D$.
Keywords: Normal families, meromorphic functions, shared values.
MSC 2000: 30D45.
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