Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 648985, 5 pages
doi:10.1155/2008/648985
Best proximity pairs for upper semicontinuous set-valued maps in hyperconvex metric spaces
A. Amini-Harandi1
, A.P. Farajzadeh2
, D. O'Regan3
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
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.