HölderKontinuität
Hölder continuity is a property of continuous functions that provides a stronger notion of smoothness than ordinary continuity. A function f: X -> Y between two metric spaces (X, d_X) and (Y, d_Y) is said to be Hölder continuous with exponent alpha (where 0 < alpha <= 1) if there exists a constant C >= 0 such that for all x, y in X, the following inequality holds: d_Y(f(x), f(y)) <= C * (d_X(x, y))^alpha.
If alpha = 1, the function is called Lipschitz continuous. If alpha < 1, the function is Hölder
Hölder continuity is important in various fields of mathematics, including partial differential equations, functional analysis, and