J. Aust. Math. Soc.  76 (2004), 141-150
A note on normality and shared values

Mingliang Fang
  Department of Mathematics
  Nanjing Normal University
  Nanjing 210097
  P. R. China
Lawrence Zalcman
  Department of Mathematics and Statistics
  Bar-Ilan University
  52900 Ramat-Gan

Let $k$ be a positive integer and $b$ a nonzero constant. Suppose that $\mathcal{F}$ is a family of meromorphic functions in a domain $D$. If each function $f\in \mathcal{F}$ has only zeros of multiplicity at least $k+2$ and for any two functions $f, g\in \mathcal{F}$, $f$ and $g$ share $0$ in $D$ and $f^{(k)}$ and $g^{(k)}$ share $b$ in $D$, then $\mathcal{F}$ is normal in $D$. The case $f\not= 0$, $f^{(k)}\not= b$ is a celebrated result of Gu.
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