18 - Lipschitz

Lipschitz Map / Continuous

Let $(X,d_X)$ and $(Y,d_Y)$ be metric space
Suppose $f:X\to Y$

$f$ is Lipschitz Map or Lipschitz Continuous if there exists constant $K\ge 0$ such that

$$d_Y(f(x),f(y))\le K{d}_X(x,y)$$

Contraction Mapping

Let $(X,d_X)$ be a metric space then

$f$ is a Contraction Mapping if $f:X\to X$ is a Lipschitz Map with constant $K\in [0,1)$