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Further Results about the Normal Family of Meromorphic Functions and Shared Sets

  • Qi, Jianming ;
  • Zhang, Guowei ;
  • Zhou, Linlin
  • Received : 2010.03.03
  • Accepted : 2011.09.23
  • Published : 2012.03.23

Abstract

Let $\mathcal{F}$ be a family of meromorphic functions in a domain D, and let $k$, $n({\geq}2)$ be two positive integers, and let $S=\{a_1,a_2,{\ldots},a_n\}$, where $a_1$, $a_2$, ${\ldots}$, $a_n$ are distinct finite complex numbers. If for each $f{\in}\mathcal{F}$, all zeros of $f$ have multiplicity at least $k+1$, $f$ and $G(f)$ share the set $S$ in $D$, where $G(f)=P(f^{(k)})+H(f)$ is a differential polynomial of $f$, then$\mathcal{F}$ is normal in $D$.

Keywords

Meromorphic functions;Nevanlinna theory;Normal family;Share value

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