Abstract
We have studied some qualitative properties such as boundedness of solutions, stability character and periodic nature of the third-order rational difference equation \begin{equation*} z_{n+1}=\delta +\dfrac{1}{z_{n}z_{n-1}z_{n-2}},\;\;\;\ \ n=0,1,... \end{equation*} with parameter $\delta $ and with arbitrary initial conditions for which the denominator is always positive. It is worth to mention that our problem is a natural extension of the Open Problem 8.2 and confirm the Conjecture 8.1 declared by A.M. Amleh, E. Camouzis and G. Ladas in On the Dynamics of a Rational Difference Equations I (International Journal of Difference Equations, Volume 3, Number 1, 2008, pp. 1-35).
Version Information
The current pdf replaces the original pdf file, first available on 5 April 2022. The new version corrects the DOI prefix to read 10.32513.
Citation
Abdul Khaliq. Sk. Sarif Hassan. "Analytical solution of a rational difference equation." Adv. Studies: Euro-Tbilisi Math. J. 15 (1) 181 - 202, March 2022. https://doi.org/10.32513/asetmj/19322008212
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