Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 19745, 7 pages
Diametrically Contractive Multivalued Mappings
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Received 1 March 2007; Accepted 2 May 2007
Academic Editor: Tomas Dominguez Benavides
Copyright © 2007 S. Dhompongsa and H. Yingtaweesittikul. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.