On the solutions of a second-order difference equation in terms of generalized Padovan sequences

Rok, strany: 2018, 625 - 638

This paper deals with the solution, stability character and asymptotic behavior of the rational difference equation \begin{equation*} x_n+1=((α x_n-1+β) / (γ x_nx_n-1)),    n \in \mathbb{N}₀, \end{equation*} where $\mathbb{N}₀=\mathbb{N}\cup \{0\}$, $α,β,γ\in\mathbb{R}⁺$, and the initial conditions $x_-1$ and $x₀$ are non zero real numbers such that their solutions are associated to generalized Padovan numbers. Also, we investigate the two-dimensional case of the this equation given by \begin{equation*} x_n+1 = ((α x_n-1 + β) / (γ y_n x_n-1)),    y_n+1 = ((α y_n-1 +β) / (γ x_n y_n-1)),   n\in \mathbb{N}₀. \end{equation*}

ISO 690:

Halim, Y., Rabago, J. 2018. On the solutions of a second-order difference equation in terms of generalized Padovan sequences. In Mathematica Slovaca, vol. 68, no.3, pp. 625-638. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0130

APA:

Halim, Y., Rabago, J. (2018). On the solutions of a second-order difference equation in terms of generalized Padovan sequences. Mathematica Slovaca, 68(3), 625-638. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0130