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Abstract: 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.



Autor: Laurentiu Leustean

Fuente: https://arxiv.org/



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