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

Abstract EN

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 un+1=F(un,un-1,un-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.