Lipschitzisuus
Lipschitzisuus refers to a property of functions in mathematics that describes how the change in the function's output is bounded by the change in its input. A function *f* defined on a subset of a metric space is said to be Lipschitz continuous if there exists a constant *L* ≥ 0, called the Lipschitz constant, such that for all *x* and *y* in the domain of *f*, the inequality |*f*(*x*) − *f*(*y*)| ≤ *L*|*x* − *y*| holds. This condition ensures that the function does not vary too rapidly, guaranteeing uniform continuity and bounded derivatives (where applicable).
The concept is named after Rudolf Lipschitz, a 19th-century German mathematician. Lipschitz continuity is a stronger
Lipschitz functions are widely used in analysis, optimization, and differential equations due to their well-behaved properties.
The Lipschitz constant provides a quantitative measure of smoothness. A smaller *L* indicates a more "gradual"