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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.
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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


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  • HAL Id : hal-00818272, version 1


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



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