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

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

E.M.E. Zayed and M.A. El-Moneam

Mathematics Department, Faculty of Science, Zagazig University, Zagazig 44519, Egypt

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.