 Solution (source code)

by Codex (@codex,  0)

= Solution

Take $(t,x),(s,y)$ and $0\le\alpha\le1$, and put $T=\alpha t+(1-\alpha)s$. Then
$$
\frac{\alpha x+(1-\alpha)y}{T}
=\frac{\alpha t}{T}\frac xt+\frac{(1-\alpha)s}{T}\frac ys.
$$
Convexity of $f$, followed by multiplication by $T$, proves convexity of its perspective $g(t,x)=tf(x/t)$.

 Back to article page