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Article Dans Une Revue Journal of Dynamics and Games Année : 2014

Asymptotic behavior of compositions of under-relaxed nonexpansive operators

Résumé

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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Dates et versions

hal-01157696 , version 1 (28-05-2015)

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Jean-Bernard Baillon, Patrick Louis Combettes, Roberto Cominetti. Asymptotic behavior of compositions of under-relaxed nonexpansive operators. Journal of Dynamics and Games, 2014, 1 (3), pp.331-346. ⟨10.3934/jdg.2014.1.331⟩. ⟨hal-01157696⟩
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