Kakutani fixed-point theorem
GPTKB entity
Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
set-valued functions
convex compact subsets of Euclidean space upper hemicontinuous correspondences |
| gptkbp:category |
fixed-point theorems
|
| gptkbp:field |
gptkb:mathematics
gptkb:topology game theory |
| gptkbp:generalizes |
gptkb:Brouwer_fixed-point_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Kakutani fixed-point theorem
|
| gptkbp:namedAfter |
gptkb:Shizuo_Kakutani
|
| gptkbp:relatedTo |
gptkb:Nash_equilibrium
gptkb:Brouwer_fixed-point_theorem |
| gptkbp:sentence |
Every upper hemicontinuous correspondence from a nonempty, compact, convex subset of Euclidean space to itself with nonempty, convex values has a fixed point.
|
| gptkbp:usedIn |
Nash equilibrium existence proof
|
| gptkbp:yearProposed |
1941
|
| gptkbp:bfsParent |
gptkb:Shizuo_Kakutani
gptkb:Masaru_Kakutani gptkb:Brewer's_theorem gptkb:Minimax_theorem |
| gptkbp:bfsLayer |
7
|