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In this paper we obtain new effective results on the Halpern iterations ofnonexpansive mappings using methods from mathematical logic or, morespecifically, proof-theoretic techniques. We give effective rates of asymptoticregularity for the Halpern iterations of nonexpansive self-mappings of nonemptyconvex sets in normed spaces. The paper presents another case study in theproject of {\em proof mining}, which is concerned with the extraction ofeffective uniform bounds from (prima-facie) ineffective proofs.

Rates of asymptotic regularity for Halpern iterations of nonexpansive mappings