Question: In this problem (X, d) is a compact metric space and f : X X is a function which has the following property: d( f

In this problem (X, d) is a compact metric space and f : X X is a function which has the following property: d( f (x), f (y) ) < d(x, y), for all x, y X such that x = y. (a) Prove that there exists a point p X, uniquely determined, such that f (p) = p. (b) Show by example that f may not satisfy the hypothesis of BCP - the Banach contraction principle, discussed in Part D of Lecture 9

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