Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 648985, 5 pages
doi:10.1155/2008/648985
Research Article

Best Proximity Pairs for Upper Semicontinuous 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, Faculty of Basic Sciences, University of Shahrekord, Shahrekord 88186-34141, Iran
2Department of Mathematics, School of Science, Razi University, Kermanshah 67149, Iran
3Department of Mathematics, College of Arts, Social Sciences and Celtic Studies, National University of Ireland, Galway, Ireland
4Department of Mathematical Sciences, College of Science, Florida Institute of Technology, Melbourne, FL 32901, USA

Received 14 July 2008; Accepted 27 October 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 map g:A→A is defined, and new existence theorems of best proximity pairs for upper semicontinuous set-valued maps with respect to a homeomorphism are proved in hyperconvex metric spaces.