International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 331-340

Stability problem of some nonlinear difference equations

Alaa E. Hamza and M. A. El-Sayed

Department of Mathematics, Faculty of Science, Cairo University, Giza 12211, Egypt

Received 10 July 1996

Copyright © 1998 Alaa E. Hamza and M. A. El-Sayed. 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.


In this paper, we investigate the asymptotic stability of the recursive sequence xn+1=α+βxn21+γxn1,n=0,1, and the existence of certain monotonic solutions of the equation xn+1=xnpf(xn,xn1,,xnk),n=0,1, which includes as a special case the rational recursive sequence xn+1=βxnp1+i=1kγixn1pr, where α0,β>0,γ>0,γi0, i=1,2,,k,i=1kγi>0, p{2,3,} and r{1,2,,p1}. The case when r=0 has been investigated by Camouzis et. al. [1], and for r=0 and p=2 by Camouzis et. al. [2].