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

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.