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International Journal of Analysis
Volume 2013 (2013), Article ID 486357, 12 pages
Research Article

Global Attractivity Results on Complete Ordered Metric Spaces for Third-Order Difference Equations

1Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood road, Pretoria 0002, South Africa
2University of Tunisia, Tunis College of Sciences and Techniques, 5 Avenue Taha Hussein, BP 56, Bab Manara, Tunis, Tunisia

Received 24 October 2012; Accepted 31 January 2013

Academic Editor: Jacques Liandrat

Copyright © 2013 Mujahid Abbas and Maher Berzig. 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.


We establish fixed-point theorems for mixed monotone mappings in the setting of ordered metric spaces which satisfy a contractive condition for all points that are related by a given ordering. We also give a global attractivity result for all solutions of the difference equation where satisfies certain monotonicity conditions with respect to the given ordering. As an application of our obtained results, we present some iterative algorithms to solve a class of matrix equations. A numerical example is also presented to test the validity of the algorithms.