Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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UNIQUENESS RESULTS ON MEROMORPHIC FUNCTIONS AND THEIR DIFFERENCE OPERATORS SHARING TARGETS WITH WEIGHT

  • Thu Thuy Hoang (Department of Mathematics Hanoi University of Civil Engineering) ;
  • Hong Nhat Nguyen (Faculty of Mathematical economics National Economics University) ;
  • Duc Thoan Pham (Department of Mathematics Hanoi University of Civil Engineering)
  • Received : 2022.03.15
  • Accepted : 2022.11.18
  • Published : 2023.03.31
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Abstract

Let f be a nonconstant meromorphic function of hyper-order strictly less than 1, and let c ∈ ℂ \ {0} such that f(z + c) ≢ f(z). We prove that if f and its exact difference ∆cf(z) = f(z + c) - f(z) share partially 0, ∞ CM and share 1 IM, then ∆cf = f, where all 1-points with multiplicities more than 2 do not need to be counted. Some similar uniqueness results for such meromorphic functions partially sharing targets with weight and their shifts are also given. Our results generalize and improve the recent important results.

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Acknowledgement

The authors wish to express their thanks to the reviewer for his/her valuable suggestions and comments which help us improve the paper. This research is funded by Hanoi University of Civil Engineering (HUCE) under grant number 16-2022/KHXD-TD.

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