更新时间:2022-09-03 20:31:24
设 $f:[0,1]\to [0,1]$.
(1). 若 $f$ 连续, 试证: $\exists\ \xi\in [0,1],\st f(\xi)=\xi$.
(2). 若 $f$ 单调递增, 试证: $\exists\ \xi\in [0,1],\st f(\xi)=\xi$.
(3). 若 $f$ 单调递减, 请问上述结论是否仍然成立? 如果成立, 请给出证明; 如果不成立, 则给出反例.
Discrete Mathematics and Its Applications,Fourth Edition
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