Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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NORMAL FAMILIES OF MEROMORPHIC FUNCTIONS WITH MULTIPLE VALUES

  • Li, Yuntong (Department of Basic Course Shaanxi Railway Institute) ;
  • Liu, Zhixiu (College of Science Nanchang Institute of Technology)
  • Received : 2016.03.10
  • Published : 2017.03.31
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Abstract

In this paper, we consider some normality criteria concerning multiple values. Let $\mathcal{F}$ be a family of meromorphic functions defined in a domain D. Let k be a positive integer and ${\psi}(z){\not\equiv}0$, ${\infty}$ be a meromorphic function in D. If, for each $f{\in}\mathcal{F}$ and $z{\in}D$, (1) $f(z){\neq}0$, and all of whose poles are multiple; (2) all zeros of $f^{(k)}(z)-{\psi}(z)$ have multiplicities at least k + 3 in D; (3) all poles of ${\psi}(z)$ have multiplicities at most k in D, then $\mathcal{F}$ is normal in D.

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References

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