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Uniqueness of Meromorphic Functions Sharing Values with Their nth Order Exact Differences

  • Z. Gao
  • R. KorhonenEmail author
  • J. Zhang
  • Y. Zhang
Article
  • 42 Downloads

Abstract

Let f(z) be a transcendental meromorphic function in the complex plane of hyper-order strictly less than 1. It is shown that if f(z) and its nth exact difference Δnf(z) (≢ 0) share three distinct periodic functions \({\rm{a, b, c}} \in \mathcal{\hat{S}}(f)\) with period 1 CM, where \(\mathcal{\hat{S}}(f) = \mathcal{S}(f)\cup\{{\infty}\}\) and \(\mathcal{S}(f)\) denotes the set of all small functions of f(z), then Δnf(z) ≡ f(z).

Key words and phrases

uniqueness meromorphic function exact difference sharing values 

Mathematics Subject Classification

30D35 39A10 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.School of Mathematics and Systems ScienceBeihang University, LMIBBeijingP. R. China
  2. 2.Department of Physics and MathematicsUniversity of Eastern FinlandJoensuuFinland

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