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A variational method in fixed point results with inwardness conditions

Authors: D. Azé and J.-N. Corvellec
Journal: Proc. Amer. Math. Soc. 134 (2006), 3577-3583
MSC (2000): Primary 47H10; Secondary 49J53
Published electronically: June 27, 2006
MathSciNet review: 2240670
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Abstract: We generalize, in a metric space setting, the result due to Lim (2000), that a weakly inward multivalued contraction, defined on a nonempty closed subset of a Banach space, has a fixed point. The simple proof of this generalization, avoiding the use of a transfinite induction as in Lim's paper, is based on Ekeland's variational principle (1974), along the lines of Hamel (1994) and Takahashi (1991). Moreover, we give a sharp estimate for the distance from any point to the fixed point set.

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Additional Information

D. Azé
Affiliation: UMR CNRS MIP, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse cedex 4, France

J.-N. Corvellec
Affiliation: Laboratoire MANO, Université de Perpignan Via Domitia, 52 avenue Paul Alduy, 66860 Perpignan cedex, France

Received by editor(s): June 24, 2005
Published electronically: June 27, 2006
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.