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Reflexivity and the Fixed-Point Property for Nonexpansive Maps

✍ Scribed by P.N. Dowling; C.J. Lennard; B. Turett

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
142 KB
Volume
200
Category
Article
ISSN
0022-247X

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✦ Synopsis

Connections between reflexivity and the fixed-point property for nonexpansive self-mappings of nonempty, closed, bounded, convex subsets of a Banach space are 1 Ε½ .

ϱ investigated. In particular, it is shown that l ⌫ for uncountable sets ⌫ and l cannot even be renormed to have the fixed-point property. As a consequence, if an Orlicz space on a finite measure space that is not purely atomic is endowed with the Orlicz norm, the Orlicz space has the fixed-point property exactly when it is reflexive.

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The Approximation of Fixed Points of Com
The Approximation of Fixed Points of Compositions of Nonexpansive Mappings in Hilbert Space
✍ Heinz H. Bauschke πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 130 KB

Determining fixed points of nonexpansive mappings is a frequent problem in mathematics and physical sciences. An algorithm for finding common fixed points of nonexpansive mappings in Hilbert space, essentially due to Halpern, is analyzed. The main theorem extends Wittmann's recent work and partially