Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 543154, 8 pages
Research Article

Coincidence Point, Best Approximation, and Best Proximity Theorems for Condensing Set-Valued Maps in Hyperconvex Metric Spaces

A. Amini-Harandi,1 A. P. Farajzadeh,2 D. O'Regan,3 and R. P. Agarwal4

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.