Common
Hölder condition
Type of continuity of a complex-valued function
Hölder condition
In mathematics, we say that a function satisfies a Hölder condition, or is α {\displaystyle \alpha } -Hölder continuous or simply Hölder continuous, if for a real or complex-valued function f {\displaystyle f} on d {\displaystyle d} -dimensional Euclidean space, i.e. f : Ω → R {\displaystyle f:\Omega \to \mathbb {R} } or C {\displaystyle \mathbb {C} } (where Ω ⊆ R d {\displaystyle \Omega \subseteq \mathbb {R} ^{d}} or C d {\displaystyle \mathbb {C} ^...
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