It is an open problem (still open) published on a Chinese mathematics magazine, but i am asking this just because i can not figure it out. I wonder if someone can help? I won't use any answers here to contact the editorial office of the magazine..
And here is the problem:
Problem. (Provider: Jiaqiang MEI, NJU) Suppose $f $ be a continuous function over $\mathbb{R}$, and if for each $x\in \mathbb{R}$ $$ \lim_{h\rightarrow 0} \frac{1}{h^3} \int_{-h}^{h} f(x+t)t\ dt =0. $$ Prove that $f$ is constant.
Any help is welcomed!
