Advances in Difference Equations
Volume 2005 (2005), Issue 3, Pages 319-332
doi:10.1155/ADE.2005.319

On a (2,2)-rational recursive sequence

Mohamed Ben Rhouma,1 M. A. El-Sayed,1,2 and Azza K. Khalifa1,2

1Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Muscat 123 Al-Khodh, Oman
2Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

Received 26 April 2004; Revised 3 November 2004

Copyright © 2005 Mohamed Ben Rhouma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the asymptotic behavior of the recursive difference equation yn+1=(α+βyn)/(1+yn−1) when the parameters α<0 and β∈ℝ. In particular, we establish the boundedness and the global stability of solutions for different ranges of the parameters α and β. We also give a summary of results and open questions on the more general recursive sequences yn+1=(a+byn)/(A+Byn−1), when the parameters a,b,A,B∈ℝ and abAB≠0.