5. Suppose that f: R - R is a Lipschitz function with a Lipschitz constant C

5. Suppose that f: R R is a Lipschitz function with a Lipschitz constant C < l. Pick some yl R and define yn+l = f (yn), for n N. Show that the resulting sequence (yn) is Cauchy, and that it converges to some y R such that f (y) = y. Prove that, for any x R, the sequence (r, f f (f ) converges to this same y.