Global Attractivity Results on Complete Ordered Metric Spaces for Third-Order Difference Equations. (27th March 2013) - Abbas, Mujahid; Berzig, Maher
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.