{"id":"https://openalex.org/W2005728959","doi":"https://doi.org/10.2478/v10037-012-0011-3","title":"Riemann Integral of Functions from R into n-dimensional Real Normed Space","display_name":"Riemann Integral of Functions from R into n-dimensional Real Normed Space","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2005728959","doi":"https://doi.org/10.2478/v10037-012-0011-3","mag":"2005728959"},"language":"en","primary_location":{"id":"doi:10.2478/v10037-012-0011-3","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-012-0011-3","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-012-0011-3","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/v10037-012-0011-3","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030176832","display_name":"Keiichi Miyajima","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/I245364917","display_name":"University of Bia\u0142ystok","ror":"https://ror.org/01qaqcf60","country_code":"PL","type":"education","lineage":["https://openalex.org/I245364917"]},{"id":"https://openalex.org/I6178835","display_name":"Ibaraki University","ror":"https://ror.org/00sjd5653","country_code":"JP","type":"education","lineage":["https://openalex.org/I6178835"]},{"id":"https://openalex.org/I65143321","display_name":"Hitachi (Japan)","ror":"https://ror.org/02exqgm79","country_code":"JP","type":"company","lineage":["https://openalex.org/I65143321"]}],"countries":["JP","PL"],"is_corresponding":false,"raw_author_name":"Keiichi Miyajima","raw_affiliation_strings":["Institute of Informatics University of Bia\u0142ystok Sosnowa 64, 15-887 Bia\u0142ystok Poland Yasunari Shidama","Shinshu University Nagano, Japan","Ibaraki University Faculty of Engineering Hitachi, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Informatics University of Bia\u0142ystok Sosnowa 64, 15-887 Bia\u0142ystok Poland Yasunari Shidama","institution_ids":["https://openalex.org/I245364917"]},{"raw_affiliation_string":"Shinshu University Nagano, Japan","institution_ids":["https://openalex.org/I137975476"]},{"raw_affiliation_string":"Ibaraki University Faculty of Engineering Hitachi, Japan","institution_ids":["https://openalex.org/I6178835","https://openalex.org/I65143321"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090121372","display_name":"Artur Korni\u0142owicz","orcid":"https://orcid.org/0000-0002-4565-9082"},"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/I245364917","display_name":"University of Bia\u0142ystok","ror":"https://ror.org/01qaqcf60","country_code":"PL","type":"education","lineage":["https://openalex.org/I245364917"]},{"id":"https://openalex.org/I6178835","display_name":"Ibaraki University","ror":"https://ror.org/00sjd5653","country_code":"JP","type":"education","lineage":["https://openalex.org/I6178835"]},{"id":"https://openalex.org/I65143321","display_name":"Hitachi (Japan)","ror":"https://ror.org/02exqgm79","country_code":"JP","type":"company","lineage":["https://openalex.org/I65143321"]}],"countries":["JP","PL"],"is_corresponding":false,"raw_author_name":"Artur Korni\u0142owicz","raw_affiliation_strings":["Institute of Informatics University of Bia\u0142ystok Sosnowa 64, 15-887 Bia\u0142ystok Poland Yasunari Shidama","Shinshu University Nagano, Japan","Ibaraki University Faculty of Engineering Hitachi, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Informatics University of Bia\u0142ystok Sosnowa 64, 15-887 Bia\u0142ystok Poland Yasunari Shidama","institution_ids":["https://openalex.org/I245364917"]},{"raw_affiliation_string":"Shinshu University Nagano, Japan","institution_ids":["https://openalex.org/I137975476"]},{"raw_affiliation_string":"Ibaraki University Faculty of Engineering Hitachi, Japan","institution_ids":["https://openalex.org/I6178835","https://openalex.org/I65143321"]}]},{"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":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2579,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.75092425,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"20","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13234","display_name":"advanced mathematical theories","score":0.9578999876976013,"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"}},"topics":[{"id":"https://openalex.org/T13234","display_name":"advanced mathematical theories","score":0.9578999876976013,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8473591208457947},{"id":"https://openalex.org/keywords/normed-vector-space","display_name":"Normed vector space","score":0.6861292123794556},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.57252436876297},{"id":"https://openalex.org/keywords/riemann-integral","display_name":"Riemann integral","score":0.5365827679634094},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.47704023122787476},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4069630205631256},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3995402753353119},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11702507734298706},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.08354136347770691},{"id":"https://openalex.org/keywords/fourier-integral-operator","display_name":"Fourier integral operator","score":0.0651281476020813}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8473591208457947},{"id":"https://openalex.org/C171739935","wikidata":"https://www.wikidata.org/wiki/Q726210","display_name":"Normed vector space","level":2,"score":0.6861292123794556},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.57252436876297},{"id":"https://openalex.org/C41833934","wikidata":"https://www.wikidata.org/wiki/Q697181","display_name":"Riemann integral","level":4,"score":0.5365827679634094},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47704023122787476},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4069630205631256},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3995402753353119},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11702507734298706},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.08354136347770691},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.0651281476020813},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.2478/v10037-012-0011-3","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-012-0011-3","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-012-0011-3","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:86b3afda-d592-4c28-8e64-0afed7479f02/oai:repozytorium.uwb.edu.pl:11320/3631","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401248","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.452.6990","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.452.6990","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/2012-20/pdf20-1/integr19.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:9ce9212210574410b719759cac3e0425","is_oa":false,"landing_page_url":"https://doaj.org/article/9ce9212210574410b719759cac3e0425","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 20, Iss 1, Pp 79-86 (2012)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/3631","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/3631","pdf_url":null,"source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"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":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/v10037-012-0011-3","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-012-0011-3","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-012-0011-3","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2005728959.pdf","grobid_xml":"https://content.openalex.org/works/W2005728959.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W79552917","https://openalex.org/W180239714","https://openalex.org/W260340778","https://openalex.org/W2042076004","https://openalex.org/W2046937081","https://openalex.org/W2061557024","https://openalex.org/W2099252149","https://openalex.org/W2105559527","https://openalex.org/W2116482758","https://openalex.org/W2127370007","https://openalex.org/W2134057927","https://openalex.org/W2136356332","https://openalex.org/W2143851127","https://openalex.org/W2150348213","https://openalex.org/W2159772409","https://openalex.org/W2160628721","https://openalex.org/W2163641194","https://openalex.org/W2296232473","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2619722956","https://openalex.org/W2140739028","https://openalex.org/W2376639130","https://openalex.org/W2348903589","https://openalex.org/W2392926382","https://openalex.org/W4245268118","https://openalex.org/W1625117912","https://openalex.org/W2479485010","https://openalex.org/W4293463489","https://openalex.org/W2005728959"],"abstract_inverted_index":{"Riemann":[0,16,37],"Integral":[1],"of":[2,30],"Functions":[3],"from":[4],"R":[5,20],"into":[6,21],"n-dimensional":[7,22],"Real":[8],"Normed":[9],"SpaceIn":[10],"this":[11,31],"article,":[12],"we":[13],"define":[14],"the":[15,28,36,43,50],"integral":[17],"on":[18],"functions":[19],"real":[23],"normed":[24],"space":[25],"and":[26],"prove":[27],"linearity":[29],"operator.":[32],"As":[33],"a":[34],"result,":[35],"integration":[38],"can":[39],"be":[40],"applied":[41],"to":[42,49],"wider":[44],"range.":[45],"Our":[46],"method":[47],"refers":[48],"[21].":[51]},"counts_by_year":[{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}