Representation of solutions of eight systems of difference equations via generalized Padovan sequences

Document Type : Research Paper

Authors

1 Ortakoy Vocational High School, Aksaray University, Aksaray, Turkey

2 Department of Mathematics, Faculty of Science, Nevsehir Haci Bektas Veli University, Nevsehir, Turkey

Abstract

We indicate 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 $a,b $ are arbitrary complex numbers, with $b\neq 0$, can be solved in the closed form in terms of generalized Padovan sequences.

Keywords