  In this paper, we obtain rates of metastability for the Tikhonov-Mann
iteration for countable families of mappings in CAT(0) spaces. This iteration
was recently defined by the author in the setting of W-hyperbolic spaces as a
generalization of the strongly convergent version of the Krasnoselskii-Mann
iteration introduced by Bot and Meier for finding common fixed points of
families of nonexpansive mappings in Hilbert spaces, and as an extension of the
Tikhonov-Mann iteration for single mappings, for which Leustean and the author
obtained rates of asymptotic regularity in W-hyperbolic spaces.
