| Hölder condition [`hel·dǝr kǝn´dish·ǝn] MATHEMATICS 1. A function f (x ) satisfies the Hölder condition in a neighborhood of a point x0 if | f (x ) - f (x0)| ≤ c |(x - x0) n|, where c and n are constants. 2. A function f (x ) satisfies a Hölder condition in an interval or in a region of the plane if f (x ) - f (y ) ≤ c x - y n for all x and y in the interval or region, where c and n are constants. |