Rates of Asymptotic Regularity for Halpern Iterations of Nonexpansive Mappings
Laurenţiu Leuştean · TUbilio (Technical University of Darmstadt) · 2007
In this paper we obtain new effective results on the Halpern iterations of nonexpansive mappings using methods from mathematical logic or, more specifically, proof-theoretic techniques. We give effective rates of asymptotic regularity for the Halpern iterations of nonexpansive self-mappings of nonempty convex sets in normed spaces. The paper presents another case study in the project of {\em proof mining}, which is concerned with the extraction of effective uniform bounds from (prima-facie) ineffective proofs.