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

Diametrically contractive multivalued mappings

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.