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On solution of a difference equation via generalized Fibonacci sequence | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 29 خرداد 1405 اصل مقاله (380.36 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.39381.5561 | ||
| نویسندگان | ||
| Ömer Aktaş* 1؛ Merve Kara2 | ||
| 1Instutite of Science, Karamanoğlu Mehmetbey University, Turkey | ||
| 2Department of Mathematics, Kamil Ozdag Science Faculty, Turkey | ||
| تاریخ دریافت: 22 مهر 1404، تاریخ بازنگری: 24 آبان 1404، تاریخ پذیرش: 25 آبان 1404 | ||
| چکیده | ||
| We consider the following the difference equation \begin{equation*} w_n=\frac{w^{r+1}_{n-2}w_{n-3}}{w_{n-1}\left(\gamma_nw_{n-4}^r+\delta_nw_{n-2}w_{n-3}\right)},\quad n\in\mathbb{N}_0, \end{equation*} where $r\in\mathbb{N},$ the initial conditions $w_{-j}$, $j=\overline{1,4}$ are non zero real numbers and $\left(\gamma_n\right)_{n\in\mathbb{N}_0}$, $\left(\delta_n\right)_{n\in\mathbb{N}_0}$ are non zero real number sequences. In addition, the solution of a more general difference equation defined by one to one continuous function is obtained. The solution of the mentioned equation is gained via a generalized Fibonacci sequence. Finally, we obtain the solution of the above difference equation when the sequences $\left(\gamma_n\right)_{n\in\mathbb{N}_0}$, $\left(\delta_n\right)_{n\in\mathbb{N}_0}$ are constant. | ||
| کلیدواژهها | ||
| Fibonacci numbers؛ difference equation؛ solution | ||
| مراجع | ||
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آمار تعداد مشاهده مقاله: 18 تعداد دریافت فایل اصل مقاله: 12 |
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