Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 762478, 17 pages
doi:10.1155/2009/762478
Research Article

Global Attractivity Results for Mixed-Monotone Mappings in Partially Ordered Complete Metric Spaces

Dž. Burgić,1 S. Kalabušić,2 and M. R. S. Kulenović3

1Department of Mathematics, University of Tuzla, 75000 Tuzla, Bosnia and Herzegovina
2Department of Mathematics, University of Sarajevo, 71000 Sarajevo, Bosnia and Herzegovina
3Department of Mathematics, University of Rhode Island, Kingston, R I 02881-0816, USA

Received 28 October 2008; Revised 17 January 2009; Accepted 9 February 2009

Academic Editor: Juan J. Nieto

Copyright © 2009 Dž. Burgić et al. 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.

Abstract

We prove fixed point theorems for mixed-monotone mappings in partially ordered complete metric spaces which satisfy a weaker contraction condition than the classical Banach contraction condition for all points that are related by given ordering. We also give a global attractivity result for all solutions of the difference equation zn+1=F(zn,zn−1), n=2,3,…, where F satisfies mixed-monotone conditions with respect to the given ordering.