Advances in Difference Equations
Volume 2010 (2010), Article ID 584890, 6 pages
doi:10.1155/2010/584890
Research Article

On a Max-Type Difference Equation

Ali Gelisken, Cengiz Cinar, and Ibrahim Yalcinkaya

Mathematics Department, Ahmet Kelesoglu Education Faculty, Selcuk University, Meram Yeni Yol, 42090 Konya, Turkey

Received 8 December 2009; Revised 20 April 2010; Accepted 23 April 2010

Academic Editor: Gaston M. N'Guérékata

Copyright © 2010 Ali Gelisken 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.

Abstract

We prove that every positive solution of the max-type difference equation xn=max⁡{A/xn-pα,B/xn-kβ}, n=0,1,2,… converges to x¯=max⁡{A1/(1+α),B1/(1+β)} where p,k are positive integers, 0<α,β<1, and 0<A,B.