Contraction Map

Definition

Consider Metric Space $(X,\mathcal{T},d)$ and a function on it $f:X\to X$. The function $f$ is contraction map if $\exists 0<\alpha <1\text{s.t.}f(f(x),f(y))\le \alpha d(x,y)$

Facts

Contraction mapping is a Continuous Function