Vertex Corrections in the Spin-fluctuation-induced Superconductivity

We evaluate vertex corrections to $T_c$ on the basis of the antiferromagnetic spin-fluctuation model of the high-$T_c$ superconductivity. It is found that the corrections are attractive in the $d_{x^2-y^2}$ channel, and they become appreciable as we go through an intermediate-coupling regime of $T_c\simeq 100$K, the maximum $T_c$ attainable in the one-loop \'Eliashberg calculation.