The fixed point property of strictly convex reflexive Banach spaces for non-expansive self-mappings (Q2923290)
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 of strictly convex reflexive Banach spaces for non-expansive self-mappings |
scientific article; zbMATH DE number 6356019
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The fixed point property of strictly convex reflexive Banach spaces for non-expansive self-mappings |
scientific article; zbMATH DE number 6356019 |
Statements
15 October 2014
0 references
Krein-Milman property
0 references
normal structure
0 references
fixed point property
0 references
diametral point
0 references
The fixed point property of strictly convex reflexive Banach spaces for non-expansive self-mappings (English)
0 references
The authors prove the followingNEWLINENEWLINE Theorem 3.7. Suppose that \(X\) is a strictly convex reflexive Banach space and \(C\) is a nonempty bounded closed convex subset of \(X\) with finitely many extreme points. Then every nonexpansive mapping \(T: C\to C\) has a fixed point.NEWLINENEWLINE Reviewer's remark: In Theorem 3.9, by the Schauder principle, every continuous (not only nonexpansive) mapping \(T: C\to C\) has a fixed point.
0 references
