{"id":"https://openalex.org/W2038158348","doi":"https://doi.org/10.1137/0802021","title":"On the Convergence of the Products of Firmly Nonexpansive Mappings","display_name":"On the Convergence of the Products of Firmly Nonexpansive Mappings","publication_year":1992,"publication_date":"1992-08-01","ids":{"openalex":"https://openalex.org/W2038158348","doi":"https://doi.org/10.1137/0802021","mag":"2038158348"},"language":"en","primary_location":{"id":"doi:10.1137/0802021","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0802021","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110258450","display_name":"Paul Tseng","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Paul Tseng","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110258450"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8577,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.85327992,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"2","issue":"3","first_page":"425","last_page":"434"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9972000122070312,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.8900139331817627},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7174429893493652},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.7075345516204834},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6734182238578796},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5986261367797852},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5923870801925659},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.5791015028953552},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5371663570404053},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.419939249753952},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4124959707260132},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3319607377052307},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33076584339141846},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.271037220954895},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19379457831382751},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06850352883338928}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8900139331817627},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7174429893493652},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.7075345516204834},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6734182238578796},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5986261367797852},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5923870801925659},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5791015028953552},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5371663570404053},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.419939249753952},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4124959707260132},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3319607377052307},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33076584339141846},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.271037220954895},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19379457831382751},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06850352883338928},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0802021","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0802021","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W218321722","https://openalex.org/W1577020372","https://openalex.org/W1964168109","https://openalex.org/W1971540397","https://openalex.org/W2006362803","https://openalex.org/W2021175931","https://openalex.org/W2021534598","https://openalex.org/W2028273959","https://openalex.org/W2038497950","https://openalex.org/W2053487511","https://openalex.org/W2086580845","https://openalex.org/W2094508696","https://openalex.org/W2144932012","https://openalex.org/W2145395365","https://openalex.org/W2156466771","https://openalex.org/W2170166494","https://openalex.org/W2171073252","https://openalex.org/W2321466613","https://openalex.org/W2329579984","https://openalex.org/W2564555264","https://openalex.org/W3048151270","https://openalex.org/W4236177621","https://openalex.org/W4301808069"],"related_works":["https://openalex.org/W2075768550","https://openalex.org/W3022218857","https://openalex.org/W2369178846","https://openalex.org/W2082716031","https://openalex.org/W2370289839","https://openalex.org/W2933494595","https://openalex.org/W3103135560","https://openalex.org/W2391553691","https://openalex.org/W2531545003","https://openalex.org/W4323058680"],"abstract_inverted_index":{"Consider":[0],"a":[1,9,41,67,80],"finite":[2],"collection":[3,31],"of":[4,26,47,91,100],"firmly":[5],"nonexpansive":[6],"self-mappings":[7],"on":[8],"Hilbert":[10],"space":[11],"whose":[12],"fixed-point":[13],"sets":[14],"intersect.":[15],"It":[16],"is":[17,57],"shown":[18,58],"that,":[19],"in":[20,79,96],"the":[21,36,45,48,53,61,71,75,92,98,101],"finite-dimensional":[22,37],"case,":[23,55],"any":[24],"iteration":[25,76],"mappings":[27,62],"drawn":[28,64],"from":[29],"this":[30],"converges.":[32],"This":[33],"resolves,":[34],"for":[35],"case":[38],"at":[39],"least,":[40],"popular":[42],"conjecture":[43],"concerning":[44],"convergence":[46],"successive":[49],"projection":[50],"method.":[51],"In":[52],"infinite-dimensional":[54],"it":[56],"that":[59],"if":[60],"are":[63,103],"according":[65],"to":[66,105],"certain":[68],"order,":[69,73],"called":[70],"quasi-cyclic":[72,83],"then":[74],"converges":[77],"weakly":[78],"sense.":[81],"The":[82],"order":[84,95],"may":[85],"be":[86],"viewed":[87],"as":[88],"an":[89],"extension":[90],"well-known":[93],"cyclic":[94],"which":[97],"lengths":[99],"cycles":[102],"permitted":[104],"grow":[106],"without":[107],"bound.":[108]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":9}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
