Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 543154, 8 pages
Coincidence Point, Best Approximation, and Best Proximity Theorems for Condensing Set-Valued Maps in Hyperconvex Metric Spaces
1Department of Mathematics, University of Shahrekord, Shahrekord 88186-34141, Iran
2Department of Mathematics, Razi University, Kermanshah 67149, Iran
3Department of Mathematics, National University of Ireland, Galway, Ireland
4Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA
Received 8 October 2008; Accepted 9 December 2008
Academic Editor: William A. Kirk
Copyright © 2008 A. Amini-Harandi 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.
In hyperconvex metric spaces, we first present a coincidence point
theorem for condensing set-valued self-maps. Then we consider the
best approximation problem and the best proximity problem for set-valued
mappings that are condensing. As an application, we derive a
coincidence point theorem for nonself-condensing set-valued maps.