  We analyze the ground state properties of Bose-Fermi mixtures using a
mean-field treatment of the boson-fermion interaction on a simple cubic
lattice. In the deep superfluid limit of the bosonic sector and the BCS regime
of the fermion sector, we derive BCS-type equations to determine the phase
diagram of the system. We find a competition between a charge density wave and
a superconducting phase. In the opposite limit, we study the Mott insulator to
superfluid transition of the bosonic sector in the presence of a staggered
density-induced alternating potential provided by the fermions, and determine
the mean-field transition line. In the two-superfluid phase of the mixture we
restrict to nearest-neighbor induced interactions between the fermions and
consider the extended Hubbard model. We perform a mean-field analysis of the
critical temperature for the formation of boson-assisted $s$-, extended $s^-$-,
$d$-, and $p$-wave pairs at fermionic half filling. We compare our results with
a recent dynamical mean-field study [Anders \emph{et al.} Phys. Rev. Lett. {\bf
109}, 206401].
