{"id":"https://openalex.org/W4311521417","doi":"https://doi.org/10.3390/sym14122563","title":"Convergence of Inexact Iterates of an Algorithm Based on Unions of Nonexpansive Mappings in Metric Spaces","display_name":"Convergence of Inexact Iterates of an Algorithm Based on Unions of Nonexpansive Mappings in Metric Spaces","publication_year":2022,"publication_date":"2022-12-05","ids":{"openalex":"https://openalex.org/W4311521417","doi":"https://doi.org/10.3390/sym14122563"},"language":"en","primary_location":{"id":"doi:10.3390/sym14122563","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14122563","pdf_url":"https://www.mdpi.com/2073-8994/14/12/2563/pdf?version=1670216791","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/12/2563/pdf?version=1670216791","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102814437","display_name":"Alexander J. Zaslavski","orcid":"https://orcid.org/0000-0002-6381-6459"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Alexander J. Zaslavski","raw_affiliation_strings":["Department of Mathematics, Technion\u2013Israel Institute of Technology, Haifa 32000, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technion\u2013Israel Institute of Technology, Haifa 32000, Israel","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102814437"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.7591,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.69804098,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"14","issue":"12","first_page":"2563","last_page":"2563"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9997000098228455,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9994000196456909,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9919999837875366,"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/iterated-function","display_name":"Iterated function","score":0.9172776937484741},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7490083575248718},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.683236837387085},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6330932974815369},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6247785687446594},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5091373324394226},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5068672299385071},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.49706700444221497},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4401404857635498},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4242458939552307},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4194890856742859},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3840511441230774},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32002636790275574},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2553226351737976},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17955809831619263},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05540674924850464}],"concepts":[{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.9172776937484741},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7490083575248718},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.683236837387085},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6330932974815369},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6247785687446594},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5091373324394226},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5068672299385071},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.49706700444221497},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4401404857635498},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4242458939552307},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4194890856742859},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3840511441230774},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32002636790275574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2553226351737976},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17955809831619263},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05540674924850464},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14122563","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14122563","pdf_url":"https://www.mdpi.com/2073-8994/14/12/2563/pdf?version=1670216791","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6cd82dd44a9d49b293ad69102d0e5d7a","is_oa":true,"landing_page_url":"https://doaj.org/article/6cd82dd44a9d49b293ad69102d0e5d7a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 12, p 2563 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/12/2563/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14122563","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14122563","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14122563","pdf_url":"https://www.mdpi.com/2073-8994/14/12/2563/pdf?version=1670216791","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4311521417.pdf"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W147294779","https://openalex.org/W961869694","https://openalex.org/W1458771408","https://openalex.org/W1487976166","https://openalex.org/W1577514385","https://openalex.org/W2020301444","https://openalex.org/W2042018553","https://openalex.org/W2065416951","https://openalex.org/W2071198970","https://openalex.org/W2294195432","https://openalex.org/W2299672774","https://openalex.org/W2484041846","https://openalex.org/W2570286572","https://openalex.org/W2590387730","https://openalex.org/W2766894413","https://openalex.org/W2788741275","https://openalex.org/W2802681976","https://openalex.org/W2942234404","https://openalex.org/W3012343072","https://openalex.org/W3081532174","https://openalex.org/W3102243629","https://openalex.org/W3141780051","https://openalex.org/W4293167479","https://openalex.org/W4294958081","https://openalex.org/W4365402051","https://openalex.org/W6697375382","https://openalex.org/W6748562029","https://openalex.org/W6782341941"],"related_works":["https://openalex.org/W2011931970","https://openalex.org/W2011780184","https://openalex.org/W4294294347","https://openalex.org/W2279239548","https://openalex.org/W115379796","https://openalex.org/W63976795","https://openalex.org/W2404658402","https://openalex.org/W2610298398","https://openalex.org/W4281992692","https://openalex.org/W2105228010"],"abstract_inverted_index":{"In":[0,42,62,79],"our":[1],"recent":[2],"paper":[3,45],"we":[4,46],"obtained":[5,32],"an":[6],"extension":[7,30],"of":[8,11,19,36,50,59,83,96,100],"a":[9,20,25,39,80,84],"theorem":[10],"Tam":[12],"(2018),":[13],"which":[14],"was":[15,31],"established":[16],"for":[17,33,53,71],"iterates":[18,35,55,101],"set-valued":[21],"paracontracting":[22],"operators":[23,90],"in":[24,38],"finite-dimensional":[26],"Euclidean":[27],"space.":[28,41],"This":[29],"exact":[34],"maps":[37],"metric":[40],"the":[43,57,63,66,72,89,94],"present":[44],"prove":[47],"two":[48],"analogs":[49],"this":[51],"result":[52],"inexact":[54],"under":[56],"presence":[58],"computational":[60],"errors.":[61],"first":[64],"result,":[65],"errors":[67],"are":[68,91],"summable,":[69],"while":[70],"second":[73],"one":[74],"they":[75],"converge":[76],"to":[77],"zero.":[78],"particular":[81],"case":[82],"Banach":[85],"space,":[86],"if":[87],"all":[88,97],"symmetric,":[92],"then":[93],"set":[95],"limit":[98],"points":[99],"is":[102],"symmetric":[103],"too.":[104]},"counts_by_year":[{"year":2023,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}