Question 43
Find all functions $f: \mathbb{R} \to \mathbb{R}$ for which
$$
f(a - b)f(c - d) + f(a - d)f(b - c) \le (a - c)f(b - d)
$$
for all real numbers $a$, $b$, $c$ and $d$.
*Note that there is only one occurrence of $f$ on the right hand side!*
$$
f(a - b)f(c - d) + f(a - d)f(b - c) \le (a - c)f(b - d)
$$
for all real numbers $a$, $b$, $c$ and $d$.
*Note that there is only one occurrence of $f$ on the right hand side!*