English

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