Question 88
Determine all functions $f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ such that for all $x, y \gt 0$
$$
f(x y) \leq \frac{x f(y)+y f(x)}{2}
$$
$$
f(x y) \leq \frac{x f(y)+y f(x)}{2}
$$
MathNet 2008-part-04 — 165 problems (EN–VI) Question 88
Math Olympiad Vault · MathNet 2008-part-04 — 165 problems (EN–VI)