Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 805460, 8 pages
doi:10.1155/2008/805460
Research Article
On the Difference Equation xn+1=α+xn−m/xnk
Department of Mathematics, Faculty of Education, Selcuk University, 42099 Meram Yeni Yol, Konya, Turkey
Received 1 July 2008; Accepted 2 October 2008
Academic Editor: Leonid Berezansky
Copyright © 2008 İbrahim Yalçinkaya. 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 global behaviour of the difference
equation of higher order xn+1=α+xn−m/xnk, n=0,1,…, where the parameters α,k∈(0,∞) and the initial values x−m,x−(m−1),…,x−2,x−1, and x0 are arbitrary positive real numbers.