Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Operation
N-operation
Binary operation
Basic binary operation
Unsigned basic binary operation
Semimetric
Metric
Metric space
Lipschitz map
Hölder map
Formulation 0
Let $M_X = (X, d_X)$ and $M_Y = (Y, d_Y)$ each be a D1107: Metric space.
A D18: Map $f : X \to Y$ is a Hölder map from $M_X$ to $M_Y$ if and only if \begin{equation} \exists \, C, \alpha > 0 : \forall \, x, y \in X : d_Y( f(x), f(y) ) \leq C d_X(x, y)^{\alpha} \end{equation}
Also known as
Hölder continuous map
Results
» R2754: Lipschitz map is Hölder continuous