Rates of asymptotic regularity for Halpern iterations of nonexpansive mappings
Functional Analysis
2007-10-10 v1 Logic
Abstract
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.
Keywords
Cite
@article{arxiv.0710.1692,
title = {Rates of asymptotic regularity for Halpern iterations of nonexpansive mappings},
author = {Laurentiu Leustean},
journal= {arXiv preprint arXiv:0710.1692},
year = {2007}
}
Comments
in C.S. Calude, G. Stefanescu, and M. Zimand (eds.), Combinatorics and Related Areas. A Collection of Papers in Honour of the 65th Birthday of Ioan Tomescu