Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 543154, 8 pages
doi:10.1155/2008/543154

Coincidence point, best approximation, and best proximity theorems for condensing set-valued maps in hyperconvex metric spaces

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

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.