The hybrid extragradient proximal-point method recently proposed by Solodov
and Svaiter has the distinctive feature of allowing a relative error toler
ance. We extend the error tolerance of this method, proving that it converg
es even if a summable error is added to the relative error. Furthermore, th
e extragradient step may be performed inexactly with a summable error. We p
resent a convergence analysis, which encompasses other well-known variation
s of the proximal-point method, previously unrelated. We establish weak glo
bal convergence under mild assumptions.