Banach's fixed-point theorem

Also called Contraction-mapping theorem.

The theorem states that when a contraction is applied to a Metric Space, there is at least one point that is fixed i.e., contracts on to itself.

Mathematically

Let $(X,d)$ be a complete metric space and let $T:X\to X$ be a contraction on $X$. Then $T$ has a unique fixed point $x\in X($ such that $T(x)=x)$.