A function `f`: **X**→**Y** between two metric spaces is said to be *contracting* if for some constant `c`<1

d_{Y}(f(a),f(b)) ≤cd_{X}(a,b).

If **X** is a complete metric space and `f`: **X**→**X** is a contracting function, then it has a unique fixed point, and iterating `f` on *any* point of **X** yields a sequence converging to that fixed point.

In fact, the above is true even if only `f ^{(k)}` (the function consisting of applying

`f`

`k`times in a row) is contracting, for some

`k`.