Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
Functions between metric spaces
|
| gptkbp:category |
Continuity (mathematics)
|
| gptkbp:defines |
A function f is Hölder continuous of order α (0 < α ≤ 1) if there exists a constant C such that |f(x) - f(y)| ≤ C|x - y|^α for all x, y in the domain.
|
| gptkbp:field |
gptkb:Mathematics
|
| gptkbp:generalizes |
Lipschitz continuity
|
| gptkbp:hasSpecialCase |
Lipschitz continuity (when α = 1)
|
| gptkbp:hasSubfield |
Analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hölder Continuity
|
| gptkbp:implies |
Uniform continuity
|
| gptkbp:introducedIn |
19th century
|
| gptkbp:namedAfter |
gptkb:Otto_Hölder
|
| gptkbp:notation |
C^{0,α}
|
| gptkbp:opposedBy |
Non-Hölder continuity
|
| gptkbp:parameter |
gptkb:Hölder_exponent
|
| gptkbp:relatedTo |
Lipschitz continuity
Uniform continuity |
| gptkbp:usedIn |
Functional analysis
Partial differential equations Fractal geometry |
| gptkbp:bfsParent |
gptkb:Regularity_Theory
|
| gptkbp:bfsLayer |
7
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