推 clouddeep:看到最後步我就知道我為啥沒解出來了....orz 02/25 23:17
※ 引述《clouddeep (fix point)》之銘言：
: 3.Letf:[0,1] → R be a continuous function.
: Consider the sequence of functions
: x
: f_0 = f, f_(n+1)(x) = ∫ f_n(t)dt ,n=0,1,2,...., x in [0,1].
: 0
: Show that f_0(x) + f_1(x) + f_2(x) +...... converges uniformly.
Proof.
因 f 在 [0,1] 上是連續，稱 |f| ≦ M for all x in [0,1]. 則
|f_1(x)| ≦ M x, |f_2(x)| ≦ M x^2/2, and ... |f_n(x)| ≦ M x^n/n!,
接下來你應該要會了～(我當年考題 = = ).
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