{"id":"https://openalex.org/W4390404828","doi":"https://doi.org/10.3390/axioms13010024","title":"On Some Properties of Multi-Valued Feng\u2013Liu-Type Operators in Metric Spaces","display_name":"On Some Properties of Multi-Valued Feng\u2013Liu-Type Operators in Metric Spaces","publication_year":2023,"publication_date":"2023-12-29","ids":{"openalex":"https://openalex.org/W4390404828","doi":"https://doi.org/10.3390/axioms13010024"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13010024","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13010024","pdf_url":"https://www.mdpi.com/2075-1680/13/1/24/pdf?version=1703844297","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/2075-1680/13/1/24/pdf?version=1703844297","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/I33800924","display_name":"Academy of Romanian Scientists","ror":"https://ror.org/04ybnj478","country_code":"RO","type":"facility","lineage":["https://openalex.org/I33800924"]},{"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":true,"raw_author_name":"Adrian Petru\u015fel","raw_affiliation_strings":["Academy of Romanian Scientists, Ilfov Street No. 3, 50044 Bucharest, Romania","Department of Mathematics, Babe\u015f-Bolyai University, Kog\u0103lniceanu Street No. 1, 400084 Cluj-Napoca, Romania"],"affiliations":[{"raw_affiliation_string":"Academy of Romanian Scientists, Ilfov Street No. 3, 50044 Bucharest, Romania","institution_ids":["https://openalex.org/I33800924"]},{"raw_affiliation_string":"Department of Mathematics, Babe\u015f-Bolyai University, 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"],"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/A5031608994","display_name":"Li-Jun Zhu","orcid":"https://orcid.org/0000-0001-8883-5034"},"institutions":[{"id":"https://openalex.org/I3019309368","display_name":"North Minzu University","ror":"https://ror.org/05xjevr11","country_code":"CN","type":"education","lineage":["https://openalex.org/I3019309368"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lijun Zhu","raw_affiliation_strings":["The Key Laboratory of Intelligent Information and Big Data Processing of NingXia Province, Health Big Data Research Institute, North Minzu University, Yinchuan 750021, China"],"affiliations":[{"raw_affiliation_string":"The Key Laboratory of Intelligent Information and Big Data Processing of NingXia Province, Health Big Data Research Institute, North Minzu University, Yinchuan 750021, China","institution_ids":["https://openalex.org/I3019309368"]}]}],"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":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.111,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.78479438,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"13","issue":"1","first_page":"24","last_page":"24"},"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"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9154000282287598,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8036373853683472},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.6120762228965759},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5423413515090942},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5133978128433228},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.49959301948547363},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.4967873692512512},{"id":"https://openalex.org/keywords/cauchy-sequence","display_name":"Cauchy sequence","score":0.45941242575645447},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.456781268119812},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.45631489157676697},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.42707327008247375},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.41285213828086853},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41248369216918945},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35288095474243164},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20017564296722412},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1498194932937622}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8036373853683472},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.6120762228965759},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5423413515090942},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5133978128433228},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.49959301948547363},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.4967873692512512},{"id":"https://openalex.org/C203192437","wikidata":"https://www.wikidata.org/wiki/Q217847","display_name":"Cauchy sequence","level":2,"score":0.45941242575645447},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.456781268119812},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.45631489157676697},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.42707327008247375},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.41285213828086853},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41248369216918945},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35288095474243164},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20017564296722412},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1498194932937622},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13010024","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13010024","pdf_url":"https://www.mdpi.com/2075-1680/13/1/24/pdf?version=1703844297","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:f305b0c533ef4f50abd986fecc708919","is_oa":true,"landing_page_url":"https://doaj.org/article/f305b0c533ef4f50abd986fecc708919","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 1, p 24 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13010024","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13010024","pdf_url":"https://www.mdpi.com/2075-1680/13/1/24/pdf?version=1703844297","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":0.7400000095367432,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G1192135257","display_name":null,"funder_award_id":"2021BEG03049","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2581736893","display_name":null,"funder_award_id":"NXYLXK2017B09","funder_id":"https://openalex.org/F4320327619","funder_display_name":"North Minzu University"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G385103938","display_name":null,"funder_award_id":"NXYLXK2017B09","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4020255992","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4889551288","display_name":null,"funder_award_id":"11861003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5677496708","display_name":null,"funder_award_id":"NXYLXK2017B09","funder_id":"https://openalex.org/F4320322877","funder_display_name":"Natural Science Foundation of Ningxia Province"},{"id":"https://openalex.org/G5760752404","display_name":null,"funder_award_id":"Projects","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8581276521","display_name":null,"funder_award_id":"11861003","funder_id":"https://openalex.org/F4320322877","funder_display_name":"Natural Science Foundation of Ningxia Province"},{"id":"https://openalex.org/G8955107213","display_name":null,"funder_award_id":"Major","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322877","display_name":"Natural Science Foundation of Ningxia Province","ror":null},{"id":"https://openalex.org/F4320327619","display_name":"North Minzu University","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4390404828.pdf"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W969407713","https://openalex.org/W1547399276","https://openalex.org/W2038301844","https://openalex.org/W2050691824","https://openalex.org/W2061856266","https://openalex.org/W2082113356","https://openalex.org/W2129941846","https://openalex.org/W2228195434","https://openalex.org/W2232335614","https://openalex.org/W2741987336","https://openalex.org/W2793758937","https://openalex.org/W2955571484","https://openalex.org/W3115235513","https://openalex.org/W3173080685","https://openalex.org/W4251507077","https://openalex.org/W6689534559"],"related_works":["https://openalex.org/W2846516035","https://openalex.org/W4249977926","https://openalex.org/W2585118952","https://openalex.org/W2012141574","https://openalex.org/W2985828462","https://openalex.org/W2354765335","https://openalex.org/W3123504591","https://openalex.org/W2369544116","https://openalex.org/W1691643469","https://openalex.org/W4244119288"],"abstract_inverted_index":{"In":[0,93],"the":[1,8,38,43,46,107,117],"context":[2],"of":[3,22,37,45,61],"a":[4,81,86],"complete":[5],"metric":[6,72],"space,":[7],"most":[9],"important":[10],"fixed-point":[11,24,55,73],"result":[12],"for":[13,26,57,75],"multi-valued":[14,27,47,62,76,118],"operators":[15,28],"was":[16],"given":[17],"in":[18,71],"1969.":[19],"Many":[20],"extensions":[21],"this":[23,58,94,103],"principle":[25],"were":[29],"proved":[30],"by":[31,105],"different":[32],"authors.":[33],"Based":[34],"on":[35,102,116],"some":[36,69],"above-mentioned":[39],"results,":[40],"we":[41,51],"introduce":[42],"notion":[44],"Feng\u2013Liu-type":[48],"operator":[49],"and":[50,67],"construct":[52],"an":[53],"abstract":[54],"theory":[56,74],"general":[59],"class":[60],"operators.":[63,77],"Our":[64],"results":[65],"extend":[66],"complement":[68],"theorems":[70,101],"An":[78],"application":[79],"to":[80,85,112],"Cauchy":[82],"problem":[83],"related":[84],"first-order":[87],"differential":[88],"inclusion":[89],"is":[90],"also":[91],"given.":[92],"case,":[95],"our":[96],"theorem":[97],"improves":[98],"several":[99],"previous":[100],"subject":[104],"relaxing":[106],"contraction-type":[108],"condition":[109],"(with":[110],"respect":[111],"its":[113],"second":[114],"argument)":[115],"right-hand":[119],"side.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2023-12-30T00:00:00"}
