Fixed Point Theory and Applications 
Volume 2007 (2007), Article ID 19745, 7 pages
doi:10.1155/2007/19745
Research Article

Diametrically Contractive Multivalued Mappings

S. Dhompongsa and H. Yingtaweesittikul

 Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Received 1 March 2007; Accepted 2 May 2007

Recommended by Tomas Dominguez Benavides

Abstract

Diametrically contractive mappings on a complete metric space are introduced by V. I. Istratescu. We extend and generalize this idea to multivalued mappings. An easy example shows that our fixed point theorem is more applicable than a former one obtained by H. K. Xu. A convergence theorem of Picard iteratives is also provided for multivalued mappings on hyperconvex spaces, thereby extending a Proinov's result.