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