olymmath

US-TST 2021 Problem 3

    Find all functions f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} that satisfy the inequality f(y)−(z−yz−xf(x)+y−xz−xf(z))≤f(x+z2)−f(x)+f(z)2f(y)-\left(\frac{z-y}{z-x} f(x)+\frac{y-x}{z-x} f(z)\right) \leq f\left(\frac{x+z}{2}\right)-\frac{f(x)+f(z)}{2} for all real numbers x<y<zx<y<z.

    Dataset text NuminaMath olympiads. Quoted with source.

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