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On a Solvable System of Difference Equations in Terms of Generalized Fibonacci Numbers

  • Arzu Yüksel and Yasin Yazlik EMAIL logo
Published/Copyright: June 15, 2023
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ABSTRACT

In this paper, we represent that the following three-dimensional system of difference equations

xn+1=αyn+aynynβzn1,yn+1=βzn+bznznγxn1,zn+1=γxn+cxnxnαyn1,  n0,

where the parameters a, b, c, α, β, γ and the initial values xi, yi, zi, i ∈ {0, 1}, are real numbers, can be solved in closed form by using transformation. We analyzed the solutions in 10 different cases depending on whether the parameters are zero or nonzero. It is noteworthy to depict that the solutions of some particular cases of this system are presented in terms of generalized Fibonacci numbers. Note that our results considerably extend and improve some recent results in the literature.

2020 Mathematics Subject Classification: 39A10; 39A20; 39A23

(Communicated by Michal Fečkan)


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Received: 2021-06-03
Accepted: 2022-04-17
Published Online: 2023-06-15

© 2023 Mathematical Institute Slovak Academy of Sciences

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