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)) ≤ c d_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.