{"id":"https://openalex.org/W4323312324","doi":"https://doi.org/10.3390/axioms12030274","title":"New Contributions to Fixed Point Theory for Multi-Valued Feng\u2013Liu Contractions","display_name":"New Contributions to Fixed Point Theory for Multi-Valued Feng\u2013Liu Contractions","publication_year":2023,"publication_date":"2023-03-06","ids":{"openalex":"https://openalex.org/W4323312324","doi":"https://doi.org/10.3390/axioms12030274"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12030274","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12030274","pdf_url":"https://www.mdpi.com/2075-1680/12/3/274/pdf?version=1678097239","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/3/274/pdf?version=1678097239","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013758899","display_name":"Adrian Petru\u015fel","orcid":"https://orcid.org/0000-0002-5629-5667"},"institutions":[{"id":"https://openalex.org/I3125347698","display_name":"Babe\u0219-Bolyai University","ror":"https://ror.org/02rmd1t30","country_code":"RO","type":"education","lineage":["https://openalex.org/I3125347698"]},{"id":"https://openalex.org/I33800924","display_name":"Academia Oamenilor de \u0218tiin\u021b\u0103 din Rom\u00e2nia","ror":"https://ror.org/04ybnj478","country_code":"RO","type":"facility","lineage":["https://openalex.org/I33800924"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Adrian Petru\u015fel","raw_affiliation_strings":["Academy of Romanian Scientists, Independen\u0163ei No. 54, 050094 Bucharest, Romania","Department of Mathematics, Babe\u015f-Bolyai University Cluj-Napoca, Kog\u0103lniceanu Street, No.1, 400084 Cluj-Napoca, Romania"],"raw_orcid":"https://orcid.org/0000-0002-5629-5667","affiliations":[{"raw_affiliation_string":"Academy of Romanian Scientists, Independen\u0163ei No. 54, 050094 Bucharest, Romania","institution_ids":["https://openalex.org/I33800924"]},{"raw_affiliation_string":"Department of Mathematics, Babe\u015f-Bolyai University Cluj-Napoca, Kog\u0103lniceanu Street, No.1, 400084 Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I3125347698"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075277076","display_name":"Gabriela Petru\u015fel","orcid":"https://orcid.org/0000-0002-8405-1977"},"institutions":[{"id":"https://openalex.org/I3125347698","display_name":"Babe\u0219-Bolyai University","ror":"https://ror.org/02rmd1t30","country_code":"RO","type":"education","lineage":["https://openalex.org/I3125347698"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Gabriela Petru\u015fel","raw_affiliation_strings":["Department of Business, Babe\u015f-Bolyai University Cluj-Napoca, Horea Street, No.7, 400174 Cluj-Napoca, Romania"],"raw_orcid":"https://orcid.org/0000-0002-8405-1977","affiliations":[{"raw_affiliation_string":"Department of Business, Babe\u015f-Bolyai University Cluj-Napoca, Horea Street, No.7, 400174 Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I3125347698"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050520268","display_name":"Jen\u2010Chih Yao","orcid":"https://orcid.org/0000-0001-9041-3375"},"institutions":[{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Jen-Chih Yao","raw_affiliation_strings":["Center for General Education, China Medical University Taichung, Taichung 40402, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for General Education, China Medical University Taichung, Taichung 40402, Taiwan","institution_ids":["https://openalex.org/I184693016"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013758899"],"corresponding_institution_ids":["https://openalex.org/I3125347698","https://openalex.org/I33800924"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":2.8987,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.90363693,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"12","issue":"3","first_page":"274","last_page":"274"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.7972050905227661},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.6920772790908813},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6597453951835632},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.6512534618377686},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5985832810401917},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5024693012237549},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32246845960617065},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30340516567230225},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.055706918239593506}],"concepts":[{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.7972050905227661},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.6920772790908813},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6597453951835632},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.6512534618377686},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5985832810401917},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5024693012237549},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32246845960617065},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30340516567230225},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.055706918239593506},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12030274","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12030274","pdf_url":"https://www.mdpi.com/2075-1680/12/3/274/pdf?version=1678097239","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:cfc3e5beb2464346947980ebe6f2e36c","is_oa":true,"landing_page_url":"https://doaj.org/article/cfc3e5beb2464346947980ebe6f2e36c","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":"Axioms, Vol 12, Iss 3, p 274 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/3/274/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12030274","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":"Axioms; Volume 12; Issue 3; Pages: 274","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12030274","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12030274","pdf_url":"https://www.mdpi.com/2075-1680/12/3/274/pdf?version=1678097239","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7699999809265137,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4323312324.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W82915671","https://openalex.org/W147294779","https://openalex.org/W341904739","https://openalex.org/W1547399276","https://openalex.org/W1601891114","https://openalex.org/W2027599389","https://openalex.org/W2038301844","https://openalex.org/W2050691824","https://openalex.org/W2051504660","https://openalex.org/W2094288700","https://openalex.org/W2129941846","https://openalex.org/W2134131261","https://openalex.org/W2793758937","https://openalex.org/W2955571484","https://openalex.org/W3035235874","https://openalex.org/W3093548059","https://openalex.org/W4205935434","https://openalex.org/W4285270338","https://openalex.org/W4300352410","https://openalex.org/W4312911507","https://openalex.org/W6603459124","https://openalex.org/W6611563816"],"related_works":["https://openalex.org/W2485369488","https://openalex.org/W3181212989","https://openalex.org/W1996521626","https://openalex.org/W2138556020","https://openalex.org/W2467751856","https://openalex.org/W1543918916","https://openalex.org/W1575298045","https://openalex.org/W3028246390","https://openalex.org/W2114723187","https://openalex.org/W2127145698"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"will":[4],"prove":[5],"several":[6],"new":[7,35],"results":[8,50],"related":[9],"to":[10,54],"the":[11,14],"concept":[12],"of":[13,57],"multi-valued":[15,29,40],"Feng\u2013Liu":[16,31,41],"contraction.":[17],"An":[18],"existence,":[19],"approximation":[20],"and":[21,33,51],"localization":[22],"fixed":[23,36],"point":[24,37],"theorem":[25,38],"for":[26,39],"a":[27,34,55],"generalized":[28],"nonself":[30],"contraction":[32],"contractions":[42],"in":[43],"vector-valued":[44],"metric":[45],"spaces":[46],"are":[47,60],"proved.":[48],"Stability":[49],"an":[52],"application":[53],"system":[56],"operatorial":[58],"inclusions":[59],"also":[61],"given.":[62]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}