  We give a quantitative analysis of a theorem due to Fenghui Wang and Huanhuan
Cui concerning the convergence of a multi-parametric version of the proximal
point algorithm. Wang and Cui's result ensures the convergence of the algorithm
to a zero of the operator. Our quantitative analysis provides explicit bounds
on the metastability (in the sense of Terence Tao) for the convergence and the
asymptotic regularity of the iteration. Moreover, our analysis bypasses the
need of sequential weak compactness and only requires a weak form of the metric
projection argument.
