  We reformulate the Eliashberg's equation for the superconducting transition
within the quasi-particle description, which takes account of the heavy
electron mass. We discuss the superconductivity of CeIr_{x}Co_{1-x}In_5 by
using such a renormalized formula. On the basis of an effective two-dimensional
Hubbard model which represents the most heavy quasi-two dimensional Fermi
surface with f-character of CeIr_{x}Co_{1-x}In_5, both normal and anomalous
self-energies are calculated up to third order with respect to the renormalized
on-site repulsion U between quasi-particles. The superconducting transition
temperature is obtained by solving the Eliashberg's equation. Reasonable
transition temperatures are obtained for moderately large U. It is found that
the momentum and frequency dependence of spin fluctuations given by RPA-like
terms gives rise to the d-wave pairing state, while the vertex correction terms
are important for obtaining reasonable transition temperatures and for
differentiating n-dependence of T_c. These obtained results seem to explain the
x-dependence of T_c in CeIr_{x}Co_{1-x}In_5 and confirm the usefulness of the
perturbation theory with respect to U.
