A shrinking projection method for nonexpansive mappings with nonsummable errors in a Hadamard space

DOI10.1007/s10479-014-1571-0zbMath1386.65150OpenAlexW2017148755MaRDI QIDQ338904

Yasunori Kimura

Publication date: 7 November 2016

Published in: Annals of Operations Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10479-014-1571-0

zbMATH Keywords

fixed pointnonexpansive mappingiterative schemeHadamard spacecomputational errorshrinking projection methodreal Hilbert ball

Mathematics Subject Classification ID

Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical solutions to equations with nonlinear operators (65J15) Special maps on metric spaces (54E40)

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Cites Work

• Convergence of a sequence of sets in a Hadamard space and the shrinking projection method for a real Hilbert ball
• Hybrid shrinking projection method for a generalized equilibrium problem, a maximal monotone operator and a countable family of relatively nonexpansive mappings
• Forcing strong convergence of proximal point iterations in a Hilbert space
• Theorems of ergodic type for \(\rho\)-nonexpansive mappings in the Hilbert ball
• On a hybrid method for a family of relatively nonexpansive mappings in a Banach space
• Approximating fixed points of \({\alpha}\)-nonexpansive mappings in uniformly convex Banach spaces and CAT(0) spaces
• Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces
• Two convergence theorems to fixed point of a nonexpansive mapping on the unit sphere of a Hilbert space
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