{"id":"https://openalex.org/W7171648937","doi":"https://doi.org/10.48550/arxiv.2607.25797","title":"On the boundedness of infinite products of relaxed projections: perturbations resilience and dynamic string-averaging","display_name":"On the boundedness of infinite products of relaxed projections: perturbations resilience and dynamic string-averaging","publication_year":2026,"publication_date":"2026-07-28","ids":{"openalex":"https://openalex.org/W7171648937","doi":"https://doi.org/10.48550/arxiv.2607.25797"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.25797","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.25797","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.25797","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017467848","display_name":"Daniel Reem","orcid":"https://orcid.org/0000-0003-3190-2720"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Reem, Daniel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5075594934","display_name":"Yair Censor","orcid":"https://orcid.org/0000-0003-2247-818X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Censor, Yair","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.7129999995231628,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.7129999995231628,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.0828000009059906,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.05079999938607216,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.7789000272750854},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6437000036239624},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.49779999256134033},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4490000009536743},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.4311999976634979},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.40380001068115234},{"id":"https://openalex.org/keywords/uniform-boundedness","display_name":"Uniform boundedness","score":0.3537999987602234}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8048999905586243},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.7789000272750854},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6437000036239624},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.49779999256134033},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49239999055862427},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4490000009536743},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4311999976634979},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.40380001068115234},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.3537999987602234},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.34549999237060547},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.3156000077724457},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.311599999666214},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.2921000123023987},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.28349998593330383},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25690001249313354},{"id":"https://openalex.org/C129301229","wikidata":"https://www.wikidata.org/wiki/Q741865","display_name":"Uniform continuity","level":3,"score":0.25380000472068787}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.25797","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.25797","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.25797","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.25797","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Very":[0],"recently":[1],"(2026),":[2],"Bauschke":[3,57],"and":[4,58,64,75,78,110,128,148],"Tung":[5,59],"extended":[6],"from":[7,26],"finite-":[8],"to":[9,102,107],"infinite-dimensional":[10],"Hilbert":[11],"spaces":[12],"a":[13,38,70,115,138,158],"result":[14,23,55,106],"published":[15],"by":[16,60,68,79,113],"Meshulam":[17],"in":[18,51,93,120,157],"1996":[19],"(following":[20],"an":[21],"earlier":[22],"of":[24,31,34,41,56,72,84,90,118,141,151,154],"Aharoni-Duchet-Wajnryb":[25],"1984)":[27],"regarding":[28,144],"the":[29,46,54,94,100,104,122,134,145],"boundedness":[30,147],"infinite":[32,152],"products":[33,153],"relaxed":[35,91],"projections":[36,92],"onto":[37],"finite":[39],"family":[40,117],"closed":[42,73,76,109],"affine":[43],"subspaces.":[44],"In":[45],"present":[47],"note":[48],"we":[49,136],"extend":[50],"various":[52],"ways":[53],"allowing":[61],"certain":[62],"perturbations":[63],"proving":[65],"perturbation":[66],"resilience,":[67],"considering":[69],"mixture":[71],"half-spaces":[74],"hyperplanes,":[77],"using":[80],"dynamic":[81,85,88],"weighted":[82],"sums":[83],"strings":[86],"(of":[87],"lengths)":[89],"iterative":[95],"process.":[96],"We":[97],"also":[98],"discuss":[99],"limitation":[101],"generalize":[103],"Bauschke-Tung":[105],"arbitrary":[108],"convex":[111],"sets":[112],"presenting":[114],"large":[116],"counterexamples":[119],"which":[121],"associated":[123],"control":[124],"is":[125],"not":[126,129],"cyclic":[127],"even":[130],"almost":[131],"cyclic.":[132],"Along":[133],"way":[135],"establish":[137],"general":[139],"theorem":[140],"independent":[142],"interest":[143],"uniform":[146,149],"unboundedness":[150],"nonexpansive":[155],"mappings":[156],"normed":[159],"space":[160],"setting.":[161]},"counts_by_year":[],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2026-07-30T00:00:00"}
