  Consider the one-dimentional Poisson equation \(-u''=f\) on the interval
\([-\pi,\pi]\), where \(f\) is an non-negative integrable function, with Robin
boundary conditions \(-u'(-\pi)+\alpha u(-\pi)=u'(\pi)+\alpha u(\pi)=0\), where
\(\alpha>0\) is a constant. In this paper we prove inequalities for the convex
integral means of solutions of this problem, using the polarization of
functions and its properties. We find solutions with maximal convex integral
means and prove their uniqueness.
