Successive averages of firmly nonexpansive mappings

Successive averages of firmly nonexpansive mappings

0.00 Avg rating0 Votes
Article ID: iaor20041881
Country: United States
Volume: 20
Issue: 2
Start Page Number: 497
End Page Number: 512
Publication Date: May 1995
Journal: Mathematics of Operations Research
Authors:
Abstract:

The problem considered here is to find common fixed points of (possibly infinitely) many firmly nonexpansive selfmappings in a Hilbert space. For this purpose we use averaged relaxations of the original mappings, the averages being Bochner integrals with respect to chosen measures. Judicious choices of such measures serve to enhance the convergence towards common fixed points. Since projection operators onto closed convex sets are firmly nonexpansive, the methods explored are applicable for solving convex feasibility problems. In particular, by varying the measures, our analysis encompasses recent developments of so-called block-iterative algorithms. We demonstrate convergence theorems which cover and extend many known results.

Reviews

Required fields are marked *. Your email address will not be published.