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In this paper we generalize the strongly convergent Krasnoselskii- Mann-typeiteration for families of nonexpansive mappings defined recently by Bo\c{t} andMeier in Hilbert spaces to the abstract setting of W - hyperbolic spaces and wecompute effective rates of asymptotic regularity for our generalization. Thisalso generalizes recent results by Leu\c{s}tean and the author on theTikhonov-Mann iteration from single mappings to families of mappings.

Rates of asymptotic regularity of the Tikhonov-Mann iteration for families of mappings