  We develop a strong-coupling theory for the superfluidity of fermion pairing
phase in a Bose-Fermi mixture. Dynamical screening, self-energy
renormalization, and a pairing gap function are included self-consistently
within the adiabatic limit (i.e., the phonon velocity is much smaller than the
Fermi velocity). An analytical solution for the transition temperature (Tc) is
derived within reasonable approximations. Using typical parameters of a
40K-87Rb mixture, we find that the calculated Tc is several times larger than
that obtained in the weak coupling theory, and can be up to several percents of
the Fermi temperature.
