  Our first result is a rate of metastability in the sense of Tao for Bruck's
iteration scheme for demicontinuous pseudocontractions in Hilbert space,
extracted from Bruck's original proof. This result generalizes earlier work in
the ongoing program of proof mining from Lipschitzian to demicontinuous
pseudocontractions. Our second main result is a metastable version of
asymptotic regularity under the additional assumption that the underlying
operator is norm-to-norm uniformly continuous on bounded subsets. These results
(and their intermediate versions given in this paper) provide a thorough
quantitative analysis of Bruck's iteration scheme for pseudocontractions in
Hilbert space.
