Let f: RR be an increasing function. Suppose that there exist a, b € R satisfy b>a and a ≤ f(a) and f(b) < b. Show that f has at least one fixed point., that is, there is some x ER such that f(x) = x. (Hint: Consider z := sup{y € R: a ≤ y ≤by ≤ f(y)} and z)

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