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On tetranacci functions with tetranacci numbers | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 07 دی 1404 اصل مقاله (337.02 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.32833.4883 | ||
| نویسندگان | ||
| Ramdoss Murali1؛ Veeramani Vithya1؛ Choonkil Park* 2 | ||
| 1Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur 635 601, Tamil Nadu, India | ||
| 2Research Institute for Convergence of Basic Science, Hanyang University, Seoul 04763, Korea | ||
| تاریخ دریافت: 09 دی 1402، تاریخ پذیرش: 27 آذر 1403 | ||
| چکیده | ||
| In this research work, we define a tetranacci function $\zeta: \mathbb{R}\to \mathbb{R}$ satisfying $$\zeta(4+\omega) = \zeta (3+\omega) + \zeta (2+\omega)+ \zeta (1+\omega)+ \zeta (\omega),$$ for all $\omega \in \mathbb{R}$. We apply induction technique to obtain useful results for tetranacci functions with tetranacci numbers and also prove that $\lim \limits_{\omega \rightarrow \infty} \frac{\zeta(\omega+1)}{\zeta(\omega)} = \delta >1$, where $\delta$ is one of the zeros of the equation $\omega^{4} - \omega^{3} - \omega^{2} - \omega -1 = 0$. | ||
| کلیدواژهها | ||
| Tetranacci number؛ Tetranacci function؛ Quotient of tetranacci functions؛ Induction method | ||
| مراجع | ||
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