Question 139
Let $\mathbb{R}^{+}$ be the set of positive real numbers. Find all function $f: \mathbb{R}^{+} \rightarrow \mathbb{R}$ such that, for all positive real number $x$ and $y$, the following conditions are satisfied:
i) $2 f(x)+2 f(y) \leq f(x+y)$.
ii) $(x+y)[y f(x)+x f(y)] \geq x y f(x+y)$.
i) $2 f(x)+2 f(y) \leq f(x+y)$.
ii) $(x+y)[y f(x)+x f(y)] \geq x y f(x+y)$.