Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 183217, 19 pages
doi:10.1155/2010/183217
Research Article

Fixed Point Results for Multivalued Maps in Metric Spaces with Generalized Inwardness Conditions

M. Frigon

Département de Mathématiques et de Statistique, Université de Montréal, C.P. 6128, succ. Centre-Ville, Montréal, (QC), H3C 3J7, Canada

Received 19 November 2009; Accepted 12 February 2010

Academic Editor: Tomonari Suzuki

Copyright © 2010 M. Frigon. 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.

Abstract

We establish fixed point theorems for multivalued mappings defined on a closed subset of a complete metric space. We generalize Lim's result on weakly inward contractions in a Banach space. We also generalize recent results of Azé and Corvellec, Maciejewski, and Uderzo for contractions and directional contractions. Finally, we present local fixed point theorems and continuation principles for generalized inward contractions.