Strong convergence of the composition of firmly nonexpansive mappings

José Márcio Machado Brito (), João Xavier Cruz Neto () and Ítalo Dowell Lira Melo ()
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José Márcio Machado Brito: Federal Institute of Piauí
João Xavier Cruz Neto: Federal University of Piauí
Ítalo Dowell Lira Melo: Federal University of Piauí

Journal of Global Optimization, 2024, vol. 90, issue 4, No 4, 907 pages

Abstract: Abstract In this paper, we provide a necessary and sufficient condition under which the compositions of finitely many firmly nonexpansive mappings in a p-uniformly convex space converge strongly. In particular, we obtain convergence results for the method of alternating projections in CAT( $$\kappa $$ κ ) spaces, with $$\kappa \ge 0$$ κ ≥ 0 . We also study the rate of convergence of the sequence generated by the method in cases where the firmly nonexpansive mappings satisfy an error bound, and the set of fixed points of these mappings is boundedly linearly regular.

Keywords: Firmly nonexpansive mappings; p-Uniformly convex space; Alternating projections; Strong convergence; CAT( $$\kappa $$ κ ) space; 47H09; 53C23; 65K05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-024-01417-w

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