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Multivalued nonexpansive mappings in Banach spaces. (English) Zbl 0988.47034

Using the technique of asymptotic centers a few fixed point theorems are proved for nonexpansive multivalued mappings acting from a nonempty closed bounded convex subset \(E\) of a Banach space \(X\) into the family of nonempty compact convex subsets of \(X\). It is assumed that considered mappings satisfy an extra condition expressed in terms of the so-called inwardness.

MSC:

47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H04 Set-valued operators
47H10 Fixed-point theorems
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References:

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