Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 812674, 5 pages
doi:10.1155/2009/812674
Research Article

On the Global Attractivity of a Max-Type Difference Equation

Ali Gelişken and Cengiz Çinar

Mathematics Department, Faculty of Education, Selcuk University, 42090 Konya, Turkey

Received 27 December 2008; Accepted 5 February 2009

Academic Editor: Yong Zhou

Copyright © 2009 Ali Gelişken and Cengiz Çinar. 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 asymptotic behavior and periodic nature of positive solutions of the difference equation xn=max⁡{A/xn−1,1/xn−3α},n=0,1,…, where A>0 and 0<α<1. We prove that every positive solution of this difference equation approaches x¯=1 or is eventually periodic with period 2.