# Contraction map

Also called a contractor. A function that brings points closer together, forming the foundation for convergence by successive approximation. Mathematically, we have $LaTeX: f: X \rightarrow X$, where $LaTeX: X$ is in a normed space, with norm of $LaTeX: x$ denoted by $LaTeX: \|x\|$. $LaTeX: f$ is a contractor if there exists a constant $LaTeX: K$ in $LaTeX: [0,1)$ such that $LaTeX: \|f(x)-f(y)\| \le K \|x-y\|$ for all $LaTeX: x$ and $LaTeX: y$ in $LaTeX: X$. See the supplement on fixed points.