{"id":"https://openalex.org/W2907198328","doi":"https://doi.org/10.1155/2019/5080723","title":"H\u00f6lder Type Inequalities for Sugeno Integrals under Usual Multiplication Operations","display_name":"H\u00f6lder Type Inequalities for Sugeno Integrals under Usual Multiplication Operations","publication_year":2019,"publication_date":"2019-01-03","ids":{"openalex":"https://openalex.org/W2907198328","doi":"https://doi.org/10.1155/2019/5080723","mag":"2907198328"},"language":"lv","primary_location":{"id":"doi:10.1155/2019/5080723","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2019/5080723","pdf_url":"https://downloads.hindawi.com/journals/afs/2019/5080723.pdf","source":{"id":"https://openalex.org/S117816480","display_name":"Advances in Fuzzy Systems","issn_l":"1687-7101","issn":["1687-7101","1687-711X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Fuzzy Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/afs/2019/5080723.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062572464","display_name":"Dug Hun Hong","orcid":"https://orcid.org/0000-0001-8268-3551"},"institutions":[{"id":"https://openalex.org/I89440247","display_name":"Myongji University","ror":"https://ror.org/00s9dpb54","country_code":"KR","type":"education","lineage":["https://openalex.org/I89440247"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Dug Hun Hong","raw_affiliation_strings":["Department of Mathematics, Myongji University, Yongin, Kyunggido 449-728, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Myongji University, Yongin, Kyunggido 449-728, Republic of Korea","institution_ids":["https://openalex.org/I89440247"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030885415","display_name":"Jae Duck Kim","orcid":"https://orcid.org/0000-0001-5313-6807"},"institutions":[{"id":"https://openalex.org/I89440247","display_name":"Myongji University","ror":"https://ror.org/00s9dpb54","country_code":"KR","type":"education","lineage":["https://openalex.org/I89440247"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Jae Duck Kim","raw_affiliation_strings":["BangMok College of Basic Studies, Myongji University, Yongin, Kyunggido 449-728, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"BangMok College of Basic Studies, Myongji University, Yongin, Kyunggido 449-728, Republic of Korea","institution_ids":["https://openalex.org/I89440247"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030885415"],"corresponding_institution_ids":["https://openalex.org/I89440247"],"apc_list":{"value":900,"currency":"USD","value_usd":900},"apc_paid":{"value":900,"currency":"USD","value_usd":900},"fwci":0.6646,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62049965,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2019","issue":null,"first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9829000234603882,"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"}},{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9613999724388123,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/algorithm","display_name":"Algorithm","score":0.4802680015563965},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26770442724227905}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4802680015563965},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26770442724227905}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2019/5080723","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2019/5080723","pdf_url":"https://downloads.hindawi.com/journals/afs/2019/5080723.pdf","source":{"id":"https://openalex.org/S117816480","display_name":"Advances in Fuzzy Systems","issn_l":"1687-7101","issn":["1687-7101","1687-711X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Fuzzy Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8321daa2b2984b5dbfaaf1096533b2cc","is_oa":true,"landing_page_url":"https://doaj.org/article/8321daa2b2984b5dbfaaf1096533b2cc","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Advances in Fuzzy Systems, Vol 2019 (2019)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2019/5080723","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/5080723","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"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":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2019/5080723","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2019/5080723","pdf_url":"https://downloads.hindawi.com/journals/afs/2019/5080723.pdf","source":{"id":"https://openalex.org/S117816480","display_name":"Advances in Fuzzy Systems","issn_l":"1687-7101","issn":["1687-7101","1687-711X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Fuzzy Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.6000000238418579}],"awards":[{"id":"https://openalex.org/G342704958","display_name":null,"funder_award_id":"funded","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G4633405725","display_name":null,"funder_award_id":"Ministry of Education (2017R1D1A1B0","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G5649674787","display_name":null,"funder_award_id":"2017R1D1A1B03027869","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2907198328.pdf","grobid_xml":"https://content.openalex.org/works/W2907198328.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1481142035","https://openalex.org/W1969748714","https://openalex.org/W1971669232","https://openalex.org/W1972236894","https://openalex.org/W1974912179","https://openalex.org/W1978734360","https://openalex.org/W1979576208","https://openalex.org/W1996949561","https://openalex.org/W2000019001","https://openalex.org/W2000229542","https://openalex.org/W2005774937","https://openalex.org/W2015194661","https://openalex.org/W2025412821","https://openalex.org/W2028119905","https://openalex.org/W2030588059","https://openalex.org/W2046757739","https://openalex.org/W2047241205","https://openalex.org/W2068804294","https://openalex.org/W2081959520","https://openalex.org/W2305751546"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2062023542","https://openalex.org/W4313731559"],"abstract_inverted_index":{"The":[0],"classical":[1],"H\u00f6lder":[2,21,26],"inequality":[3],"shows":[4],"an":[5],"interesting":[6,45],"upper":[7],"bound":[8],"for":[9,29,36,130],"Lebesgue":[10,100],"integral":[11],"of":[12,15,43,147],"the":[13,44,49,99,145,148],"product":[14],"two":[16],"functions.":[17,41,120,138],"This":[18],"paper":[19],"proposes":[20],"type":[22,27,128],"inequalities":[23,28,129],"and":[24,94,112,118],"reverse":[25],"Sugeno":[30,131],"integrals":[31,132],"under":[32],"usual":[33],"multiplication":[34],"operations":[35],"nonincreasing":[37,117,134],"concave":[38,119,135],"or":[39,136],"convex":[40,137],"One":[42],"results":[46],"is":[47,98],"that":[48],"inequality,":[50],"<mml:math":[51,86,95,103,109,113],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[52,87,96,104,110,114],"id=\"M1\"><mml:msup><mml:mrow><mml:mfenced":[53],"separators=\"|\"><mml:mrow><mml:mo":[54,63],"stretchy=\"false\">(</mml:mo><mml:mi>S</mml:mi><mml:mo":[55,64,76],"stretchy=\"false\">)</mml:mo><mml:mrow><mml:msubsup><mml:mo":[56,65,77],"stretchy=\"false\">\u222b</mml:mo><mml:mrow><mml:mn":[57,66,78],"mathvariant=\"normal\">0</mml:mn></mml:mrow><mml:mrow><mml:mn":[58,67,79],"mathvariant=\"normal\">1</mml:mn></mml:mrow></mml:msubsup><mml:mrow><mml:mi>f</mml:mi><mml:mo":[59,80],"stretchy=\"false\">(</mml:mo><mml:mi>x</mml:mi><mml:msup><mml:mrow><mml:mo":[60,69],"stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup><mml:mi>d</mml:mi><mml:mi>\u03bc</mml:mi></mml:mrow></mml:mrow></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mn":[61],"mathvariant=\"normal\">1</mml:mn><mml:mo>/</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mfenced":[62],"mathvariant=\"normal\">1</mml:mn></mml:mrow></mml:msubsup><mml:mrow><mml:mi>g</mml:mi><mml:mo":[68],"stretchy=\"false\">)</mml:mo></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msup><mml:mi>d</mml:mi><mml:mi>\u03bc</mml:mi></mml:mrow></mml:mrow></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mn":[70],"mathvariant=\"normal\">1</mml:mn><mml:mo>/</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:msup><mml:mo>\u2264</mml:mo><mml:mfenced":[71],"separators=\"|\"><mml:mrow><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mi>q</mml:mi><mml:mo>/</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:msup><mml:mo>-</mml:mo><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mn":[72],"mathvariant=\"normal\">1</mml:mn></mml:mrow></mml:mfenced><mml:mo>\u2228</mml:mo><mml:mfenced":[73],"separators=\"|\"><mml:mrow><mml:msup><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mi>p</mml:mi><mml:mo>/</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:msup><mml:mo>-</mml:mo><mml:msup><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mn":[74],"mathvariant=\"normal\">1</mml:mn></mml:mrow></mml:mfenced><mml:mo":[75],"stretchy=\"false\">(</mml:mo><mml:mi>x</mml:mi><mml:mo":[81,83],"stretchy=\"false\">)</mml:mo><mml:mi>g</mml:mi><mml:mo":[82],"stretchy=\"false\">)</mml:mo><mml:mi>d</mml:mi><mml:mi>\u03bc</mml:mi></mml:mrow></mml:mrow><mml:mo>,</mml:mo></mml:math>":[84],"where":[85],"id=\"M2\"><mml:mn":[88],"mathvariant=\"normal\">1</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mi":[89],"mathvariant=\"normal\">\u221e</mml:mi><mml:mo>,</mml:mo><mml:mn":[90],"mathvariant=\"normal\">1</mml:mn><mml:mo>/</mml:mo><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mn":[91],"mathvariant=\"normal\">1</mml:mn><mml:mo>/</mml:mo><mml:mi>q</mml:mi><mml:mo>=</mml:mo><mml:mn":[92],"mathvariant=\"normal\">1</mml:mn></mml:math>":[93],"id=\"M3\"><mml:mrow><mml:mi>\u03bc</mml:mi></mml:mrow></mml:math>":[97],"measure":[101],"on":[102],"id=\"M4\"><mml:mi":[105],"mathvariant=\"double-struck\">R</mml:mi><mml:mo>,</mml:mo></mml:math>":[106],"holds":[107],"if":[108],"id=\"M5\"><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:math>":[111],"id=\"M6\"><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>":[115],"are":[116,141],"As":[121],"a":[122],"special":[123],"case,":[124],"we":[125],"consider":[126],"Cauchy-Schwarz":[127],"involving":[133],"Some":[139],"examples":[140],"provided":[142],"to":[143],"illustrate":[144],"validity":[146],"proposed":[149],"inequalities.":[150]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}
