Asymptotic regularity results for a viscosity version of Halpern-type iterations

Recently, Cheval and Leustean computed linear rates of asymptotic regularity for a viscosity version of Halpern-type iterations generated by a nonexpansive self-mapping of a metric space assuming that it has a fixed point. In the present paper, we show that their result is valid without this assumpt...

Full description

Saved in:
Bibliographic Details
Published inOptimization Vol. 74; no. 10; pp. 2457 - 2468
Main Author Zaslavski, Alexander J.
Format Journal Article
LanguageEnglish
Published Taylor & Francis 27.07.2025
Subjects
Asymptotic regularity
Halpern iteration
nonexpansive mapping
strict contraction
Online AccessGet full text

Cover

More Information
Summary:Recently, Cheval and Leustean computed linear rates of asymptotic regularity for a viscosity version of Halpern-type iterations generated by a nonexpansive self-mapping of a metric space assuming that it has a fixed point. In the present paper, we show that their result is valid without this assumption. It is enough either to assume the existence of a bounded orbit of the nonexpansive mapping or the existence of a bounded sequence of approximate fixed points of the mapping.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2024.2347973