[Everyday Mathematics]20150121
2015-01-07 10:22
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设 $f\in C[0,1]$ 适合 $$\bex xf(y)+yf(x)\leq 1,\quad\forall\ x,y\in [0,1]. \eex$$ 试证: $$\bex \int_0^1 f(x)\rd x\leq \frac{\pi}{4}. \eex$$
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