A function f: XY between two metric spaces is said to be contracting if for some constant c<1

dY(f(a),f(b)) ≤ c dX(a,b).

If X is a complete metric space and f: XX 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.

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