2013/04/26 by Jean-Bernard Baillon, Baillon, J. -B., Patrick L. Combettes +3
Computer Science · Mathematics · #47H09 #47H10 #47H20 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1304.7078
openalex publication_date 2013/04/26 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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.