Uniform Asymptotic Regularity for Mann Iterates

Forfattere

  • Ulrich Kohlenbach

DOI:

https://doi.org/10.7146/brics.v9i10.21728

Resumé

In a previous paper we obtained an effective quantitative analysis of a theorem due to Borwein, Reich and Shafrir on the asymptotic behavior of general Krasnoselski-Mann iterations for nonexpansive self-mappings of convex sets C in arbitrary normed spaces. We used this result to obtain a new strong uniform version of Ishikawa's theorem for bounded C . In this paper we give a qualitative improvement of our result in the unbounded case and prove the uniformity result for the bounded case under the weaker assumption that C contains a point x whose Krasnoselski-Mann iteration (x_n) is bounded.
We also consider more general iterations for which asymptotic regularity is known only for uniformly convex spaces (Groetsch). We give uniform effective bounds for (an extension of) Groetsch's theorem which generalize previous results by Kirk/Martinez-Yanez and the author.

Downloads

Publiceret

2002-03-05

Citation/Eksport

Kohlenbach, U. (2002). Uniform Asymptotic Regularity for Mann Iterates. BRICS Report Series, 9(10). https://doi.org/10.7146/brics.v9i10.21728

Nummer

Nr. 10 (2002): RS-10 Uniform Asymptotic Regularity for Mann Iterates

Sektion

Artikler

Licens

Authors who publish with this journal agree to the following terms:

    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

    1. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

  1. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).