Global Attractivity Results on Complete Ordered Metric Spaces for Third-Order Difference Equations. (27th March 2013)

• Record Type: Journal Article
• Authors: Abbas, Mujahid; Berzig, Maher
• Other Names: Liandrat Jacques Academic Editor.
• Is Part Of: International journal of analysis. Volume 2013(2013)
• Publication Date: 2013-03-27
• Subjects: Mathematical analysis -- Periodicals; 515.05
• DOI: 10.1155/2013/486357
• Languages: English
• ISSNs: 2314-498X

Abstract

Abstract : 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 u n + 1 = F ( u n, u n - 1, u n - 2 ), n = 2, 3, …, where F 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.