International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 23618, 12 pages
doi:10.1155/2007/23618
Research Article

On the Rational Recursive Sequence xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i)

E. M. E. Zayed1,2 and M. A. El-Moneam1

1Mathematics Department, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
2Mathematics Department, Faculty of Science, Taif University, P.O. Box 888, El-Taif 5700, Hawai, Saudi Arabia

Received 13 August 2006; Revised 22 January 2007; Accepted 22 January 2007

Academic Editor: Martin J. Bohner

Copyright © 2007 E. M. E. Zayed and M. A. El-Moneam. 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

The main objective of this paper is to study the boundedness character, the periodic character, the convergence, and the global stability of the positive solutions of the difference equation xn+1=(A+∑i=0kαixn−i)/(B+∑i=0kβixn−i), n=0,1,2,…, where A, B, αi, βi and the initial conditions x−k,...,x−1,x0 are arbitrary positive real numbers, while k is a positive integer number.