Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Meromorphic Functions Sharing a Nonzero Value with their Derivatives

  • Li, Xiao-Min (School of Mathematical Sciences, Ocean University Of China) ;
  • Ullah, Rahman (School of Mathematical Sciences, Ocean University Of China) ;
  • Piao, Da-Xiong (School of Mathematical Sciences, Ocean University Of China) ;
  • Yi, Hong-Xun (Department of Mathematics, Shandong University)
  • Received : 2014.07.30
  • Accepted : 2014.11.19
  • Published : 2015.03.23
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Abstract

Let f be a transcendental meromorphic function of finite order in the plane such that $f^{(m)}$ has finitely many zeros for some positive integer $m{\geq}2$. Suppose that $f^{(k)}$ and f share a CM, where $k{\geq}1$ is a positive integer, $a{\neq}0$ is a finite complex value. Then f is an entire function such that $f^{(k)}-a=c(f-a)$, where $c{\neq}0$ is a nonzero constant. The results in this paper are concerning a conjecture of Bruck [5]. An example is provided to show that the results in this paper, in a sense, are the best possible.

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References

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