\begin{definition}[Definition:Contraction Mapping (Metric Space)]
Let $\struct {X, d_1}$ and $\struct {Y, d_2}$ be metric spaces.
Let $f: X \to Y$ be a mapping.
Then $f$ is a '''contraction (mapping)''' {{iff}} there exists $\kappa \in \R: 0 \le \kappa < 1$ such that:
:$\forall x, y \in X: \map {d_2} {\map f x, \map f y} \le \kappa \map {d_1} {x, y}$
That is, $f$ is Lipschitz continuous for a Lipschitz constant less than $1$.
\end{definition}