{"id":"https://openalex.org/W2097639331","doi":"https://doi.org/10.2478/v10037-008-0008-0","title":"The First Mean Value Theorem for Integrals","display_name":"The First Mean Value Theorem for Integrals","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2097639331","doi":"https://doi.org/10.2478/v10037-008-0008-0","mag":"2097639331"},"language":"en","primary_location":{"id":"doi:10.2478/v10037-008-0008-0","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-008-0008-0","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-008-0008-0","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.2478/v10037-008-0008-0","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057236933","display_name":"Keiko Narita","orcid":null},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]},{"id":"https://openalex.org/I4210113483","display_name":"National Institute of Technology, Gifu College","ror":"https://ror.org/025b2hx26","country_code":"JP","type":"education","lineage":["https://openalex.org/I4210113483","https://openalex.org/I4210120810"]},{"id":"https://openalex.org/I4210149837","display_name":"Hirosaki National Hospital","ror":"https://ror.org/03qrrp624","country_code":"JP","type":"healthcare","lineage":["https://openalex.org/I4210137409","https://openalex.org/I4210149837"]},{"id":"https://openalex.org/I4210162928","display_name":"\u014ctani University","ror":"https://ror.org/05b7rex33","country_code":"JP","type":"education","lineage":["https://openalex.org/I4210162928"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Keiko Narita","raw_affiliation_strings":["Yasunari Shidama Shinshu University Nagano, Japan","Hirosaki-city Aomori, Japan","Gifu National College of Technology Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yasunari Shidama Shinshu University Nagano, Japan","institution_ids":["https://openalex.org/I137975476","https://openalex.org/I4210162928"]},{"raw_affiliation_string":"Hirosaki-city Aomori, Japan","institution_ids":["https://openalex.org/I4210149837"]},{"raw_affiliation_string":"Gifu National College of Technology Japan","institution_ids":["https://openalex.org/I4210113483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015450295","display_name":"Noboru Endou","orcid":"https://orcid.org/0000-0002-5922-2332"},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]},{"id":"https://openalex.org/I4210113483","display_name":"National Institute of Technology, Gifu College","ror":"https://ror.org/025b2hx26","country_code":"JP","type":"education","lineage":["https://openalex.org/I4210113483","https://openalex.org/I4210120810"]},{"id":"https://openalex.org/I4210149837","display_name":"Hirosaki National Hospital","ror":"https://ror.org/03qrrp624","country_code":"JP","type":"healthcare","lineage":["https://openalex.org/I4210137409","https://openalex.org/I4210149837"]},{"id":"https://openalex.org/I4210162928","display_name":"\u014ctani University","ror":"https://ror.org/05b7rex33","country_code":"JP","type":"education","lineage":["https://openalex.org/I4210162928"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Noboru Endou","raw_affiliation_strings":["Yasunari Shidama Shinshu University Nagano, Japan","Gifu National College of Technology Japan","Hirosaki-city Aomori, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yasunari Shidama Shinshu University Nagano, Japan","institution_ids":["https://openalex.org/I137975476","https://openalex.org/I4210162928"]},{"raw_affiliation_string":"Gifu National College of Technology Japan","institution_ids":["https://openalex.org/I4210113483"]},{"raw_affiliation_string":"Hirosaki-city Aomori, Japan","institution_ids":["https://openalex.org/I4210149837"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055549852","display_name":"Yasunari Shidama","orcid":"https://orcid.org/0000-0001-5634-0838"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yasunari Shidama","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.1521863,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"16","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9965999722480774,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9965999722480774,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.8724859356880188},{"id":"https://openalex.org/keywords/mean-value-theorem","display_name":"Mean value theorem (divided differences)","score":0.6082925796508789},{"id":"https://openalex.org/keywords/mean-value","display_name":"Mean value","score":0.5048180222511292},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.48548343777656555},{"id":"https://openalex.org/keywords/fundamental-theorem-of-calculus","display_name":"Fundamental theorem of calculus","score":0.4572867751121521},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3769541084766388},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37575480341911316},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3659646213054657},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30629581212997437},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23751357197761536},{"id":"https://openalex.org/keywords/brouwer-fixed-point-theorem","display_name":"Brouwer fixed-point theorem","score":0.14202165603637695},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.13418683409690857},{"id":"https://openalex.org/keywords/picard\u2013lindel\u00f6f-theorem","display_name":"Picard\u2013Lindel\u00f6f theorem","score":0.13167595863342285}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8724859356880188},{"id":"https://openalex.org/C139588767","wikidata":"https://www.wikidata.org/wiki/Q17098096","display_name":"Mean value theorem (divided differences)","level":4,"score":0.6082925796508789},{"id":"https://openalex.org/C2988626262","wikidata":"https://www.wikidata.org/wiki/Q2796622","display_name":"Mean value","level":2,"score":0.5048180222511292},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.48548343777656555},{"id":"https://openalex.org/C81150689","wikidata":"https://www.wikidata.org/wiki/Q1217677","display_name":"Fundamental theorem of calculus","level":4,"score":0.4572867751121521},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3769541084766388},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37575480341911316},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3659646213054657},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30629581212997437},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23751357197761536},{"id":"https://openalex.org/C146147875","wikidata":"https://www.wikidata.org/wiki/Q1144897","display_name":"Brouwer fixed-point theorem","level":3,"score":0.14202165603637695},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.13418683409690857},{"id":"https://openalex.org/C206929604","wikidata":"https://www.wikidata.org/wiki/Q530152","display_name":"Picard\u2013Lindel\u00f6f theorem","level":3,"score":0.13167595863342285},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/v10037-008-0008-0","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-008-0008-0","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-008-0008-0","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.149.2474","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.2474","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mizar.org/fm/2008-16/pdf16-1/mesfunc7.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:b50ae57846c84e958c76a081bf5a19ae","is_oa":false,"landing_page_url":"https://doaj.org/article/b50ae57846c84e958c76a081bf5a19ae","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 16, Iss 1, Pp 51-55 (2008)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2478/v10037-008-0008-0","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-008-0008-0","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-008-0008-0","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2097639331.pdf","grobid_xml":"https://content.openalex.org/works/W2097639331.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W180239714","https://openalex.org/W1483101703","https://openalex.org/W1619732349","https://openalex.org/W2105559527","https://openalex.org/W2136356332","https://openalex.org/W2150348213","https://openalex.org/W2163011897","https://openalex.org/W2163641194","https://openalex.org/W2296232473","https://openalex.org/W2552817710","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2350657505","https://openalex.org/W2392559853","https://openalex.org/W2110548308","https://openalex.org/W2394391654","https://openalex.org/W2387523140","https://openalex.org/W2378038670","https://openalex.org/W2352159927","https://openalex.org/W2372279473","https://openalex.org/W2370010044","https://openalex.org/W2377934825"],"abstract_inverted_index":{"The":[0,19],"First":[1],"Mean":[2],"Value":[3],"Theorem":[4],"for":[5,16],"IntegralsIn":[6],"this":[7],"article,":[8],"we":[9],"prove":[10],"the":[11,25,28],"first":[12],"mean":[13],"value":[14],"theorem":[15],"integrals":[17],"[16].":[18],"formalization":[20],"of":[21,27],"various":[22],"theorems":[23],"about":[24],"properties":[26],"Lebesgue":[29],"integral":[30],"is":[31],"also":[32],"presented.MML":[33],"identifier:":[34],"MESFUNC7,":[35],"version:":[36],"7.8.09":[37],"4.97.1001":[38]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}