A variational method in fixed point results with inwardness conditions

Azé, D.; Corvellec, J.-N.

doi:10.1090/S0002-9939-06-08744-2

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.

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