  We compare the solutions of two one-dimensional Poisson problems on an
interval with Robin boundary conditions, one with given data, and one where the
data has been symmetrized. When the Robin parameter is positive and the
symmetrization is symmetric decreasing rearrangement, we prove that the
solution to the symmetrized problem has larger increasing convex means. When
the Robin parameter equals zero (so that we have Neumann boundary conditions)
and the symmetrization is decreasing rearrangement, we similarly show that the
solution to the symmetrized problem has larger convex means.
