TY - JOUR
T1 - Asymptotic behavior of compositions of under-relaxed nonexpansive operators
AU - Baillon, Jean Bernard
AU - Combettes, Patrick L.
AU - Cominetti, Roberto
N1 - Publisher Copyright:
© American Institute of Mathematical Sciences.
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84920984357&partnerID=8YFLogxK
U2 - 10.3934/jdg.2014.1.331
DO - 10.3934/jdg.2014.1.331
M3 - Article
AN - SCOPUS:84920984357
SN - 2164-6074
VL - 1
SP - 331
EP - 346
JO - Journal of Dynamics and Games
JF - Journal of Dynamics and Games
IS - 3
ER -