  In the setting of hyperbolic spaces, we show that the convergence of
Browder-type sequences and Halpern iterations respectively entail the
convergence of their viscosity version with a Rakotch map. We also show that
the convergence of a hybrid viscosity version of the Krasnoselskii-Mann
iteration follows from the convergence of the Browder type sequence. Our
results follow from proof-theoretic techniques (proof mining). From an analysis
of theorems due to T. Suzuki, we extract a transformation of rates for the
original Browder type and Halpern iterations into rates for the corresponding
viscosity versions. We show that these transformations can be applied to
earlier quantitative studies of these iterations. From an analysis of a theorem
due to H.-K. Xu, N. Altwaijry and S. Chebbi, we obtain similar results.
Finally, in uniformly convex Banach spaces we study a strong notion of
accretive operator due to Brezis and Sibony and extract an uniform modulus of
uniqueness for the property of being a zero point. In this context, we show
that it is possible to obtain Cauchy rates for the Browder type and the Halpern
iterations (and hence also for their viscosity versions).
