The fixed point property and unbounded sets in Banach spaces (Q993635)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The fixed point property and unbounded sets in Banach spaces |
scientific article; zbMATH DE number 5788313
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The fixed point property and unbounded sets in Banach spaces |
scientific article; zbMATH DE number 5788313 |
Statements
The fixed point property and unbounded sets in Banach spaces (English)
0 references
20 September 2010
0 references
Let \(C\) be a real Hilbert space and let be a closed convex subset on \(H\). \textit{W. O. Ray} [Trans. Am. Math. Soc. 258, 531--537 (1980; Zbl 0433.47026)] proved that every nonexpansive mapping of \(C\) into itself has a fixed point in \(C\) iff \(C\) is bounded. The authors in the paper under review prove a counterpart of Ray's theorem in the setting of Banach spaces for the class of nonspreading mappings.
0 references
Banach space
0 references
nonspreading mapping
0 references
fixed point
0 references
