In mathematics, we say that a function satisfies a Hölder condition, or is -Hölder continuous or simply Hölder continuous, if for a real or complex-valued function on -dimensional Euclidean space, i.e. or , when there are real constants , , such that for all . More generally, the condition can be formulated for functions between any two metric spaces. The number is called the exponent of the Hölder condition. A function on an interval satisfying the condition with is constant. If , then the function satisfies a Lipschitz condition. For any , the condition implies the function is uniformly continuous. The condition is named after Otto Hölder. If , the function is simply bounded.