contraction

A contraction mapping on a metric space $(\mathcal{X}, d)$ is a function $f$ such that

for all $x, y \in \mathcal{X}$ and for some $q\in [0, 1)$, called the Lipschitz constant of the map. The Banach fixed point theorem implies that any such mapping can be thought of as pulling its input closer to some unique fixed point $x^*$ such that $x^* = f(x^*)$.