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