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

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  • Mujahid Abbas
  • Maher Berzig

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 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.

Suggested Citation

  • Mujahid Abbas & Maher Berzig, 2013. "Global Attractivity Results on Complete Ordered Metric Spaces for Third-Order Difference Equations," International Journal of Analysis, Hindawi, vol. 2013, pages 1-12, March.
    • Handle: RePEc:hin:ijanal:486357
    DOI: 10.1155/2013/486357
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    References listed on IDEAS

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    1. Engwerda, J.C., 1993. "On the existence of a positive definite solution of the matrix equation X = ATX-1A = I," Other publications TiSEM 9d762863-0dfe-4aeb-8a13-5, Tilburg University, School of Economics and Management.
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