Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 607926, 9 pages
doi:10.1155/2008/607926
Research Article

Best Proximity Pairs Theorems for Continuous Set-Valued Maps

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 15 July 2008; Accepted 16 September 2008

Academic Editor: Nan-jing Huang

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.

Abstract

A best proximity pair for a set-valued map F:A⊸B with respect to a set-valued map G:A⊸A is defined, and a new existence theorem of best proximity pairs for continuous set-valued maps is proved in nonexpansive retract metric spaces. As an application, we derive a coincidence point theorem.