Asymptotic behavior of compositions of under-relaxed nonexpansive operators
Functional Analysis
2013-04-29 v1
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.
Keywords
Cite
@article{arxiv.1304.7078,
title = {Asymptotic behavior of compositions of under-relaxed nonexpansive operators},
author = {J. -B. Baillon and P. L. Combettes and R. Cominetti},
journal= {arXiv preprint arXiv:1304.7078},
year = {2013}
}