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dc.contributor.authorFirmino, Paulo
dc.contributor.authorPinto, Pedro
dc.date.accessioned2024-07-15T12:55:48Z
dc.date.available2024-07-15T12:55:48Z
dc.date.issued2024-07-15
dc.identifier.urihttp://publications.mfo.de/handle/mfo/4157
dc.description.abstractWe generalize the alternating Halpern-Mann iteration to countably infinite families of nonexpansive maps and prove its strong convergence towards a common fixed point in the general nonlinear setting of Hadamard spaces. Our approach is based on a quantitative perspective which allowed to circumvent prevalent troublesome arguments and in the end provide a simple convergence proof. In that sense, discussing both the asymptotic regularity and the strong convergence of the iteration in quantitative terms, we furthermore provide low complexity uniform rates of convergence and of metastability (in the sense of T. Tao). In CAT(0) spaces, we obtain linear and quadratic uniform rates of convergence. Our results are made possible by proof-theoretical insights of the research program proof mining and extend several previous theorems in the literature.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2024-07
dc.subjectHyperbolic Spacesen_US
dc.subjectCAT(0) Spacesen_US
dc.subjectUniform Rates of Convergenceen_US
dc.subjectMetastabilityen_US
dc.subjectProof Miningen_US
dc.titleThe Alternating Halpern-Mann Iteration for Families of Mapsen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2024-07
local.scientificprogramOWLF 2024en_US
local.series.idOWP-2024-07en_US
local.subject.msc47en_US
local.subject.msc03en_US
dc.identifier.urnurn:nbn:de:101:1-2407221241151.248742616818
dc.identifier.ppn1895996457


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