In mathematics, a real or complex-valued function f on d-dimensional Euclidean space satisfies a Hölder condition, or is Hölder continuous, when there are real constants C ≥ 0, α > 0, such that | f − f | ≤ C ‖ x − y ‖ α {\displaystyle |f-f|\leq C\|x-y\|^{\alpha }} for all x and y in the domain of f. Wikipedia