Motivated by the recent discoveries of ferromagnetic and non-centrosymmetric
superconductors, we present a mean-field theory for a superconductor that
\textit{both} lacks inversion symmetry and displays ferromagnetism, a scenario
which is believed to be realized in UIr. We study the interplay between the
order parameters to clarify how superconductivity is affected by the presence
of ferromagnetism and spin-orbit coupling. One of our key findings is that the
spin-orbit coupling seems to enhance both ferromagnetism and superconductivity
in all spin channels. We discuss our results in the context of the heavy
fermion superconductor UIr and analyze possible symmetries of the order
parameter by the group theory method.Comment: 4 pages, 1 figure. Accepted for publication in Phys. Rev.