We set $\Psi(u) = \exp(-u^{2})$ for all real $u$. Prove that for all $x, y \in \mathbb{R}$, $$\Psi(\lambda x + (1-\lambda) y) \geq \Psi(x)^{\lambda} \Psi(y)^{1-\lambda}$$
We set $\Psi(u) = \exp(-u^{2})$ for all real $u$. Prove that for all $x, y \in \mathbb{R}$,
$$\Psi(\lambda x + (1-\lambda) y) \geq \Psi(x)^{\lambda} \Psi(y)^{1-\lambda}$$