International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 1, Pages 1-6
doi:10.1155/S0161171201010614
On the recursive sequence xn+1=−1/xn+A/xn−1
Matematički Fakultet, Studentski Trg 16, Beograd 11000, Serbia and Montenegro
Received 20 July 2000; Revised 8 November 2000
Copyright © 2001 Stevo Stević. 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 periodic character of solutions of the
nonlinear difference equation xn+1=−1/xn+A/xn−1. We give sufficient conditions under which every
positive solution of this equation converges to a period two
solution. This confirms a conjecture in the work of DeVault et al.
(2000).