Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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The Normality of Meromorphic Functions with Multiple Zeros and Poles Concerning Sharing Values

  • WANG, YOU-MING (Department of Applied Mathematics, College of Science, Hunan Agricultural University)
  • Received : 2013.10.22
  • Accepted : 2013.12.13
  • Published : 2015.09.23
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Abstract

In this paper we study the problem of normal families of meromorphic functions concerning shared values. Let F be a family of meromorphic functions in the plane domain $D{\subseteq}{\mathbb{C}}$ and n, k be two positive integers such that $n{\geq}k+1$, and let a, b be two finite complex constants such that $a{\neq}0$. Suppose that (1) $f+a(f^{(k)})^n$ and $g+a(g^{(k)})^n$ share b in D for every pair of functions f, $g{\in}F$; (2) All zeros of f have multiplicity at least k + 2 and all poles of f have multiplicity at least 2 for each $f{\in}F$ in D; (3) Zeros of $f^{(k)}(z)$ are not the b points of f(z) for each $f{\in}F$ in D. Then F is normal in D. And some examples are provided to show the result is sharp.

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References

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