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Towards the fixed point property for superreflexive spaces
Published online by Cambridge University Press: 17 April 2009
Abstract
A Banach space X is said to have property (Sm) if every metrically convex set A ⊂ X which lies on the unit sphere and has diameter not greater than one can be (weakly) separated from zero by a functional. We show that this geometrical condition is closely connected with the fixed point property for nonexpansive mappings in superreflexive spaces.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 64 , Issue 3 , December 2001 , pp. 435 - 444
- Copyright
- Copyright © Australian Mathematical Society 2001
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