Definition:Contraction Mapping

Definition

Let $(X,d_1),(Y,d_2)$ be metric spaces and $f : X \to Y$ a mapping.

Then $f$ is a contraction if there exists $0 \leq \kappa < 1$ such that:

$d_2(f(x),f(y)) \leq \kappa d_1 (x,y)\quad \forall x,y \in X$