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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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[1] K.T. Atanassov, V. Atanassova, A.G. Shannon, and J.C. Turner, New Visual Perspectives on Fibonacci Numbers, World Sci. Publ. Co., New Jersey, 2002. [2] J.J. Bravo, M. Diaz and C.A. Gomez, Pillai’s problem with k-Fibonacci and Pell numbers, J. Difference Equ. Appl. 27 (2021), no. 10, 1434–1455. [3] R.A. Dunlap, The Golden Ratio and Fibonacci Numbers, World Sci. Publ. Co., New Jersey, 1997. [4] M. Feinberg, Fibonacci-tribonacci, Fibonacci Quart. 1 (1963), no. 3, 70–74. [5] J.S. Han, H.S. Kim, and J. Neggers, The Fibonacci norm of a positive integer n-observations and conjectures, Int. J. Number Theory 6 (2010), no. 2, 371–385. [6] J.S. Han, H.S. Kim, and J. Neggers, Fibonacci sequences in groupoids, Adv. Difference Equ. 2012 (2012), Paper No. 19. [7] J.S. Han, H.S. Kim, and J. Neggers, On Fibonacci functions with Fibonacci numbers, Adv. Difference Equ. 2012 (2012), Paper No. 126. [8] S.M. Jung, Hyers-Ulam stability of Fibonacci functional equation, Bull. Iran. Math. Soc. 35 (2009), no. 2, 217–227. [9] H.S. Kim and J. Neggers, Fibonacci means and golden section mean, Comput. Math. Appl. 56 (2008), no. 1, 228–232. [10] C. Kizilates and T. Kone, On higher order Fibonacci quaternions, J. Anal. 29 (2021), no. 4, 1071–1082. [11] E. T. Lipka and M.A. Ulas, A Fibonacci type sequence with Prouhet-Thue-Morse coefficients, J. Difference Equ. Appl. 28 (2022), no. 5, 695–715. [12] M.N. Parizi and M. Eshaghi Gordji, On tribonacci functions and tribonacci numbers, Int. J. Math. Comput. Sci. 11 (2016), no. 1, 23–32. | ||
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