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

Best proximity pairs theorems for continuous set-valued maps

A. Amini-Harandi1 , A.P. Farajzadeh2 , D. O'Regan3 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

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.