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Discrete Dynamics in Nature and Society
Volume 2010, Article ID 235808, 14 pages
http://dx.doi.org/10.1155/2010/235808
Research Article

Quantitative Bounds for Positive Solutions of a Stević Difference Equation

College of Computer Science, Chongqing University, Chongqing 400044, China

Received 8 November 2009; Revised 5 March 2010; Accepted 7 April 2010

Academic Editor: Leonid Berezansky

Copyright © 2010 Wanping Liu and Xiaofan Yang. 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

This paper studies the behavior of positive solutions to the following particular case of a difference equation by Stević 𝑥 𝑛 + 1 = 𝐴 + 𝑥 𝑝 𝑛 / 𝑥 𝑝 𝑘 + 1 𝑛 𝑘 , 𝑛 0 , where 𝐴 ,, , and presents theoretically computable explicit lower and upper bounds for the positive solutions to this equation. Besides, a concrete example is given to show the computing approaches which are effective for small parameters. Some analogous results are also established for the corresponding Stević max-type difference equation.