A variational method in fixed point results with inwardness conditions
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- by D. Azé and J.-N. Corvellec PDF
- Proc. Amer. Math. Soc. 134 (2006), 3577-3583 Request permission
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.References
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Additional Information
- D. Azé
- Affiliation: UMR CNRS MIP, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse cedex 4, France
- Email: aze@mip.ups-tlse.fr
- J.-N. Corvellec
- Affiliation: Laboratoire MANO, Université de Perpignan Via Domitia, 52 avenue Paul Alduy, 66860 Perpignan cedex, France
- Email: corvellec@univ-perp.fr
- Received by editor(s): June 24, 2005
- Published electronically: June 27, 2006
- Communicated by: Jonathan M. Borwein
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 3577-3583
- MSC (2000): Primary 47H10; Secondary 49J53
- DOI: https://doi.org/10.1090/S0002-9939-06-08744-2
- MathSciNet review: 2240670