Asymptotic behavior of compositions of under-relaxed nonexpansive operators

Jean Bernard Baillon, Patrick L. Combettes, Roberto Cominetti

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish
Pages (from-to)331-346
Number of pages16
JournalJournal of Dynamics and Games
Issue number3
StatePublished - 2014


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