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A variational method in fixed point results with inwardness conditions
Author(s):
D.
Azé;
J.-N.
Corvellec
Journal:
Proc. Amer. Math. Soc.
134
(2006),
3577-3583.
MSC (2000):
Primary 47H10;
Secondary 49J53
Posted:
June 27, 2006
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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.
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
DOI:
10.1090/S0002-9939-06-08744-2
PII:
S 0002-9939(06)08744-2
Received by editor(s):
June 24, 2005
Posted:
June 27, 2006
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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