MMN-3234
On eight solvable systems of difference equations in terms of generalized Padovan sequences
M. Kara; Y. Yazlik;Abstract
In this study we show that the systems of difference equations $$
x_{n+1}=f^{-1}\big( af\left( p_{n-1}\right)+bf\left( q_{n-2}\right) \big) , \ \ y_{n+1}=f^{-1}\big( af\left( r_{n-1}\right)+bf\left( s_{n-2}\right) \big),$$ $n\in \mathbb{N}_{0}$, where the sequences $p_{n}$, $q_{n}$, $r_{n}$, $s_{n}$ are some of the sequences $x_{n}$ and $y_{n}$, $f : D_f \longrightarrow \mathbb{R}$ be a $ ``1-1" $ continuous function on its domain $D_f \subseteq \mathbb{R}$, initial values $x_{-j}$, $y_{-j}$, $j\in\{0,1,2\}$ are arbitrary real numbers in $D_f$, and the parameters and $a,b $ are arbitrary complex numbers, with $b\neq 0$, can be solved in the closed form in terms of generalized Padovan sequences. Some analitical examples are given to demonstrate the theoretical results.
Vol. 22 (2021), No. 2, pp. 695-708