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Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
contraction mapping theorem
|
| gptkbp:appliesTo |
complete metric space
contraction mapping |
| gptkbp:category |
fixed-point theorems
theorems in analysis |
| gptkbp:field |
gptkb:mathematics
analysis metric space theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Banach fixed-point theorem
|
| gptkbp:implies |
existence and uniqueness of fixed point
|
| gptkbp:namedAfter |
gptkb:Stefan_Banach
|
| gptkbp:provides |
method to find fixed point by iteration
|
| gptkbp:publishedIn |
gptkb:Fundamenta_Mathematicae
|
| gptkbp:relatedTo |
gptkb:Brouwer_fixed-point_theorem
gptkb:Picard–Lindelöf_theorem gptkb:Schauder_fixed-point_theorem |
| gptkbp:state |
Every contraction mapping on a complete metric space has a unique fixed point.
|
| gptkbp:usedIn |
computer science
numerical analysis partial differential equations iterative methods dynamic programming |
| gptkbp:yearProposed |
1922
|
| gptkbp:bfsParent |
gptkb:Stefan_Banach
|
| gptkbp:bfsLayer |
4
|