Advances in Difference Equations
Volume 2008 (2008), Article ID 238068, 6 pages
Research Article

Stability of Solutions for a Family of Nonlinear Difference Equations

Taixiang Sun,1 Hongjian Xi,1,2 and Caihong Han1

1College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China
2Department of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi 530003, China

Received 8 September 2007; Accepted 31 January 2008

Academic Editor: Mariella Cecchi

Copyright © 2008 Taixiang Sun et al. 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.


We consider the family of nonlinear difference equations: xn+1=(i=13fi(xn,,xnk)+f4(xn,,xnk)f5(xn,,xnk))/(f1(xn,,xnk)f2(xn,,xnk)+i=35fi(xn,,xnk)), n=0,1,, where fiC((0,+)k+1,(0,+)), for i{1,2,4,5}, f3C([0,+)k+1,(0,+)), k{1,2,} and the initial values xk,xk+1,,x0(0,+). We give sufficient conditions under which the unique equilibrium x¯=1 of these equations is globally asymptotically stable, which extends and includes corresponding results obtained in the cited references.