The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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UNIQUENESS RELATED TO HIGHER ORDER DIFFERENCE OPERATORS OF ENTIRE FUNCTIONS

  • Xinmei Liu (School of Mathematics and Statistics, Fujian Normal University) ;
  • Junfan Chen (School of Mathematics and Statistics, Fujian Normal University)
  • Received : 2022.10.18
  • Accepted : 2023.02.03
  • Published : 2023.02.28
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Abstract

In this paper, by using the difference analogue of Nevanlinna's theory, the authors study the shared-value problem concerning two higher order difference operators of a transcendental entire function with finite order. The following conclusion is proved: Let f(z) be a finite order transcendental entire function such that λ(f - a(z)) < ρ(f), where a(z)(∈ S(f)) is an entire function and satisfies ρ(a(z)) < 1, and let 𝜂(∈ ℂ) be a constant such that ∆𝜂n+1 f(z) ≢ 0. If ∆𝜂n+1 f(z) and ∆𝜂n f(z) share ∆𝜂n a(z) CM, where ∆𝜂n a(z) ∈ S ∆𝜂n+1 f(z), then f(z) has a specific expression f(z) = a(z) + BeAz, where A and B are two non-zero constants and a(z) reduces to a constant.

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Acknowledgement

The authors would like to thank the referees for their thorough review with constructive suggestions and valuable comments on the paper. Project supported by the Natural Science Foundation of Fujian Province (2021J01651).

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