Kyungpook Mathematical Journal

  • 제52권1호
  • /
  • Pages.39-47
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  • 2012
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Further Results about the Normal Family of Meromorphic Functions and Shared Sets

  • Qi, Jianming (Department of Mathematics and Physics, Shanghai Dianji University) ;
  • Zhang, Guowei (School of Mathematics and Statistics, Anyang Normal University) ;
  • Zhou, Linlin (Department of Mathematics, Zhenjiang watercraft college)
  • 투고 : 2010.03.03
  • 심사 : 2011.09.23
  • 발행 : 2012.03.23
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초록

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 $D$.

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참고문헌

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