{"id":"https://openalex.org/W2762462576","doi":"https://doi.org/10.1137/17m1134986","title":"Regular Sequences of Quasi-Nonexpansive Operators and Their Applications","display_name":"Regular Sequences of Quasi-Nonexpansive Operators and Their Applications","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2762462576","doi":"https://doi.org/10.1137/17m1134986","mag":"2762462576"},"language":"en","primary_location":{"id":"doi:10.1137/17m1134986","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1134986","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1710.00534","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082463321","display_name":"Andrzej Cegielski","orcid":"https://orcid.org/0000-0002-1840-4455"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andrzej Cegielski","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057413218","display_name":"Simeon Reich","orcid":"https://orcid.org/0000-0003-0780-1559"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simeon Reich","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5071059710","display_name":"Rafa\u0142 Zalas","orcid":"https://orcid.org/0000-0003-0193-9610"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rafa\u0142 Zalas","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5082463321"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02892964,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"2","first_page":"1508","last_page":"1532"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9377999901771545,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9298999905586243,"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/hilbert-space","display_name":"Hilbert space","score":0.8287732601165771},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8009805679321289},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.613667368888855},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6128560304641724},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5938062071800232},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5730886459350586},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5592954158782959},{"id":"https://openalex.org/keywords/linear-operators","display_name":"Linear operators","score":0.5236197113990784},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.510015606880188},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.49977946281433105},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.4941451847553253},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48826074600219727},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4670839309692383},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4520929455757141},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40472131967544556},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3113694190979004},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3088665306568146},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2700923681259155},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17554455995559692},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06069135665893555}],"concepts":[{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.8287732601165771},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8009805679321289},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.613667368888855},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6128560304641724},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5938062071800232},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5730886459350586},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5592954158782959},{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.5236197113990784},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.510015606880188},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.49977946281433105},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.4941451847553253},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48826074600219727},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4670839309692383},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4520929455757141},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40472131967544556},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3113694190979004},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3088665306568146},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2700923681259155},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17554455995559692},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06069135665893555},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/17m1134986","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1134986","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1710.00534","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.00534","pdf_url":"https://arxiv.org/pdf/1710.00534","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2762462576","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1710.00534.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1710.00534","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1710.00534","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1710.00534","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.00534","pdf_url":"https://arxiv.org/pdf/1710.00534","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"score":0.550000011920929,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G2942734666","display_name":null,"funder_award_id":"389/12","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G4017111610","display_name":null,"funder_award_id":"820/17","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G6942865434","display_name":null,"funder_award_id":"N00014-12-1-0997","funder_id":"https://openalex.org/F4320323721","funder_display_name":"Technion-Israel Institute of Technology"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320323721","display_name":"Technion-Israel Institute of Technology","ror":"https://ror.org/03qryx823"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2762462576.pdf"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1123046575","https://openalex.org/W1210354003","https://openalex.org/W1547403762","https://openalex.org/W1595803699","https://openalex.org/W1710475132","https://openalex.org/W1853237406","https://openalex.org/W1963892562","https://openalex.org/W1971915361","https://openalex.org/W1974451927","https://openalex.org/W1975181084","https://openalex.org/W1988262431","https://openalex.org/W2001504661","https://openalex.org/W2005693246","https://openalex.org/W2009126525","https://openalex.org/W2022993401","https://openalex.org/W2025424390","https://openalex.org/W2033511209","https://openalex.org/W2038085385","https://openalex.org/W2053487511","https://openalex.org/W2054796771","https://openalex.org/W2132614631","https://openalex.org/W2134851358","https://openalex.org/W2138146018","https://openalex.org/W2149059117","https://openalex.org/W2154746110","https://openalex.org/W2183947807","https://openalex.org/W2246928227","https://openalex.org/W2291131262","https://openalex.org/W2336954693","https://openalex.org/W2570286572","https://openalex.org/W2598135565","https://openalex.org/W2598996488","https://openalex.org/W2767229208","https://openalex.org/W2962704982","https://openalex.org/W2963462530","https://openalex.org/W3104490314","https://openalex.org/W4250507917"],"related_works":["https://openalex.org/W2963755278","https://openalex.org/W3157647781","https://openalex.org/W2136805774","https://openalex.org/W2916531788","https://openalex.org/W2381443067","https://openalex.org/W2342653183","https://openalex.org/W2942267486","https://openalex.org/W2182964648","https://openalex.org/W2072413528","https://openalex.org/W2003460352","https://openalex.org/W2753485015","https://openalex.org/W3034426600","https://openalex.org/W3103135560","https://openalex.org/W2981342028","https://openalex.org/W2170936021","https://openalex.org/W2094975457","https://openalex.org/W2471731337","https://openalex.org/W2134757943","https://openalex.org/W3026248761","https://openalex.org/W2887445458"],"abstract_inverted_index":{"In":[0],"this":[1,51],"paper":[2],"we":[3,53,99],"present":[4],"a":[5],"systematic":[6],"study":[7],"of":[8,11,29,36,47,69,103,106],"regular":[9,27,104],"sequences":[10,28,105],"quasi-nonexpansive":[12],"operators":[13,107],"in":[14,20,22,50,75,86],"Hilbert":[15],"space.":[16],"We":[17,31],"are":[18,88],"interested,":[19],"particular,":[21,76],"weakly,":[23],"boundedly,":[24],"and":[25,45,58,65,80],"linearly":[26],"operators.":[30,48],"show":[32,54,100],"that":[33,55],"the":[34,37,91],"type":[35],"regularity":[38,60],"is":[39],"preserved":[40],"under":[41],"relaxations,":[42],"convex":[43],"combinations,":[44],"products":[46],"Moreover,":[49],"connection,":[52],"weak,":[56,63],"bounded,":[57],"linear":[59,66],"lead":[61],"to":[62,77,96,108],"strong,":[64],"convergence,":[67],"respectively,":[68],"various":[70],"iterative":[71,79],"methods.":[72],"This":[73],"applies,":[74],"block":[78],"string":[81],"averaging":[82],"projection":[83],"methods,":[84],"which,":[85],"principle,":[87],"based":[89],"on":[90],"abovementioned":[92],"algebraic":[93],"operations":[94],"applied":[95],"projections.":[97],"Finally,":[98],"an":[101],"application":[102],"variational":[109],"inequality":[110],"problems.":[111]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
