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

Abstract

In this paper we generalize the strongly convergent Krasnoselskii- Mann-type iteration for families of nonexpansive mappings defined recently by Boţ and Meier in Hilbert spaces to the abstract setting of W - hyperbolic spaces and we compute effective rates of asymptotic regularity for our generalization. This also generalizes recent results by Leuştean and the author on the Tikhonov-Mann iteration from single mappings to families of mappings.