Prove the following, without using the derivative of g in the proof. Let g 2 C[a, b] be such that g(x) 2 [a, b] for all x 2 [a, b]. Suppose, in addition, that g satisfies a Lipschitz condition on the interval [a, b] with Lipschitz constant L < 1. Then for any number p0 in [a, b] the sequence defined by pn = g(pn?1), n 1 converges to the unique fixed point p in [a, b].