Question: Prove that if f is continuous on [0, 1] and satisfies 0 s f(x) 1 there, then f has a fixed point that is,

Prove that if f is continuous on [0, 1] and satisfies 0 s f(x) ≤ 1 there, then f has a fixed point that is, there is a number c in [0, 1] such that f(c) = c.

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