| Citation: |
Mensure Şen, Yasin Yazlik, Merve Kara. ON A SYSTEM OF DIFFERENCE EQUATIONS DEFINED BY THE CONTINUOUS AND STRICTLY MONOTONE FUNCTIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3690-3703. doi: 10.11948/20250012
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ON A SYSTEM OF DIFFERENCE EQUATIONS DEFINED BY THE CONTINUOUS AND STRICTLY MONOTONE FUNCTIONS
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Abstract
In this paper, we solve the following difference equations system
$ \begin{align*} \begin{cases} \omega_{n+1}=g^{-1}\left( g\left( \omega_{n}\right) \dfrac{\zeta_{1}h\left( \vartheta_{n}\right)+\eta_{1}h\left( \vartheta_{n-1}\right) }{\mu_{1}h\left( \vartheta_{n}\right)+\xi_{1}h\left( \vartheta_{n-1}\right)}\right), \\ \vartheta_{n+1}=h^{-1}\left( h\left( \vartheta_{n}\right) \dfrac{\zeta_{2}g\left( \omega_{n}\right)+\eta_{2}g\left( \omega_{n-1}\right) }{\mu_{2}g\left( \omega_{n}\right)+\xi_{2}g\left( \omega_{n-1}\right)}\right) , \end{cases} n\in \mathbb{N}_{0}, \end{align*} $
where the coefficients $ \mu_{k}^2+\xi_{k}^2\neq0 $, $ \zeta_{k} $, $ \eta_{k} $, $ \mu_{k} $, $ \xi_{k} $, for $ k\in\{1,2\} $ are real numbers, the initial values $ \omega_{-j} $, $ \vartheta_{-j} $, for $ j\in\{0,1\} $ are real numbers, $ g $ and $ h $ are continuous and strictly monotone functions, $ g\left( \mathbb{R}\right) =\mathbb{R} $, $ h\left( \mathbb{R}\right) =\mathbb{R} $, $ g\left( 0\right) =0 $, $ h\left( 0\right) =0 $, in explicit form depending on whether or not the parameters are equal to $ 0 $.
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Keywords:
- Difference equations systems /
- solution /
- monotone functions
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References
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Mensure Şen, Yasin Yazlik, Merve Kara. ON A SYSTEM OF DIFFERENCE EQUATIONS DEFINED BY THE CONTINUOUS AND STRICTLY MONOTONE FUNCTIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3690-3703. doi: 10.11948/20250012
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