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Journals / Ikonion Journal of Mathematics / 2020 / Cilt: 2 - Sayı: 1

A solvable system of nonlinear difference equations

Abdullah ŞAHİNKAYA
İbrahim YALÇINKAYA
Durhasan Turgut TOLLU
Pages
10–20
Publication Date
2020-07-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also, we investigate the asymptotic behavior of the solutions by using these formulae and give some numerical examples which verify our theoretical result.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we show that the following systems of nonlinear difference equations x_{n+1}=((x_{n}y_{n}+a)/(x_{n}+y_{n})),y_{n+1}=((y_{n}z_{n}+a)/(y_{n}+z_{n})),z_{n+1}=((z_{n}x_{n}+a)/(z_{n}+x_{n})) for n∈ℕ₀ where a∈[0,∞) and the initial values x₀, y₀, z₀ are real numbers, can be solved in explicit form.
📊
Key Findings & Data:In this paper, we show that the following systems of nonlinear difference equations x_{n+1}=((x_{n}y_{n}+a)/(x_{n}+y_{n})),y_{n+1}=((y_{n}z_{n}+a)/(y_{n}+z_{n})),z_{n+1}=((z_{n}x_{n}+a)/(z_{n}+x_{n})) for n∈ℕ₀ where a∈[0,∞) and the initial values x₀, y₀, z₀ are real numbers, can be solved in explicit form.
💡
Conclusion & Impact:Also, we investigate the asymptotic behavior of the solutions by using these formulae and give some numerical examples which verify our theoretical result.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Asymptotic behavior · explicit solution · nonlinear difference equation

Abstract

In this paper, we show that the following systems of nonlinear difference equations x_{n+1}=((x_{n}y_{n}+a)/(x_{n}+y_{n})),y_{n+1}=((y_{n}z_{n}+a)/(y_{n}+z_{n})),z_{n+1}=((z_{n}x_{n}+a)/(z_{n}+x_{n})) for n∈ℕ₀ where a∈[0,∞) and the initial values x₀, y₀, z₀ are real numbers, can be solved in explicit form. Also, we investigate the asymptotic behavior of the solutions by using these formulae and give some numerical examples which verify our theoretical result.

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Cite This Article

ŞAHİNKAYA, A., YALÇINKAYA, İ., TOLLU, D. T. (2020). A solvable system of nonlinear difference equations. Ikonion Journal of Mathematics, Cilt: 2 - Sayı: 1, 10–20. https://ajindex.com/articles/764546

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References (9)

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