Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 19745, 7 pages
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

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.