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Abstract and Applied Analysis
Volume 2012, Article ID 240378, 57 pages
http://dx.doi.org/10.1155/2012/240378
Research Article

Positive Solutions and Iterative Approximations for a Nonlinear Two-Dimensional Difference System with Multiple Delays

1Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, China
2Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
3Department of Mathematics, Dong-A University, Busan 614-714, Republic of Korea

Received 16 March 2012; Accepted 30 May 2012

Academic Editor: Josef Diblík

Copyright © 2012 Zeqing Liu 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

This paper studies the nonlinear two-dimensional difference system with multiple delays . Using the Banach fixed point theorem and a few new analysis techniques, we show the existence of uncountably many bounded positive solutions for the system, suggest Mann iterative algorithms with errors, and discuss the error estimates between the positive solutions and iterative sequences generated by the Mann iterative algorithms. Examples to illustrates the results are included.