HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Reports

Asymptotic behavior of compositions of under-relaxed nonexpansive operators

Abstract : In general there exists no relationship between the fixed point sets of the composition and of the average of a family of nonexpansive operators in Hilbert spaces. In this paper, we establish an asymptotic principle connecting the cycles generated by under-relaxed compositions of nonexpansive operators to the fixed points of the average of these operators. In the special case when the operators are projectors onto closed convex sets, we prove a conjecture by De Pierro which has so far been established only for projections onto affine subspaces.
Complete list of metadata

Cited literature [18 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00818272
Contributor : Patrick Louis Combettes Connect in order to contact the contributor
Submitted on : Friday, April 26, 2013 - 2:47:22 PM
Last modification on : Friday, May 6, 2022 - 4:50:07 PM
Long-term archiving on: : Saturday, July 27, 2013 - 4:10:09 AM

File

1.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00818272, version 1

Citation

Jean-Bernard Baillon, Patrick Louis Combettes, Roberto Cominetti. Asymptotic behavior of compositions of under-relaxed nonexpansive operators. 2013. ⟨hal-00818272⟩

Share

Metrics

Record views

145

Files downloads

78