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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.30 No.1

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Uniqueness related to Higher Order Difference Operators of Entire Functions

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2023, v.30 no.1, pp.43-65
https://doi.org/https://doi.org/10.7468/jksmeb.2023.30.1.43
Xinmei Liu
Junfan Chen
Xinmei, L. , & Junfan, C. (2023). Uniqueness related to Higher Order Difference Operators of Entire Functions, 30(1), 43-65, https://doi.org/https://doi.org/10.7468/jksmeb.2023.30.1.43

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.

keywords
transcendental entire function, sharing value, higher order difference operator, uniqueness

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

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