Probably too easy for experienced members, but at least for someone this might be a good exercise to get acquainted with a technique.
be a midpoint convex
Show that then this function fulfills
and any rational
Sketch of the solution:
It is relatively easy to see, that it suffices to show
for any integer k (and any choice of
is a straightforward induction.
then we denote
. Now from
by a simple algebraic manipulation.