Open Access

Diametrically Contractive Multivalued Mappings

Fixed Point Theory and Applications20072007:019745

https://doi.org/10.1155/2007/19745

Received: 1 March 2007

Accepted: 2 May 2007

Published: 14 June 2007

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.

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Authors’ Affiliations

(1)
Department of Mathematics, Faculty of Science, Chiang Mai University

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Copyright

© S. Dhompongsa and H. Yingtaweesittikul. 2007

This article is published under license to BioMed Central Ltd. 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.