{"id":"https://openalex.org/W2762269280","doi":"https://doi.org/10.1080/00029890.2018.1436837","title":"A Gronwall-type Trigonometric Inequality","display_name":"A Gronwall-type Trigonometric Inequality","publication_year":2018,"publication_date":"2018-04-12","ids":{"openalex":"https://openalex.org/W2762269280","doi":"https://doi.org/10.1080/00029890.2018.1436837","mag":"2762269280"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2018.1436837","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1436837","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1710.01270","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"A. G. Smirnov","orcid":"https://orcid.org/0000-0002-2498-568X"},"institutions":[{"id":"https://openalex.org/I118517470","display_name":"P.N. Lebedev Physical Institute of the Russian Academy of Sciences","ror":"https://ror.org/01jkd3546","country_code":"RU","type":"facility","lineage":["https://openalex.org/I118517470","https://openalex.org/I1313323035","https://openalex.org/I2800498218","https://openalex.org/I4210096333"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"A. G. Smirnov","raw_affiliation_strings":["I. E. Tamm Theory Department, P. N. Lebedev Physical Institute, Leninsky prospect 53, Moscow 119991, Russia"],"affiliations":[{"raw_affiliation_string":"I. E. Tamm Theory Department, P. N. Lebedev Physical Institute, Leninsky prospect 53, Moscow 119991, Russia","institution_ids":["https://openalex.org/I118517470"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I118517470"],"apc_list":null,"apc_paid":null,"fwci":1.0428,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.71391209,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"125","issue":"5","first_page":"453","last_page":"456"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.4311999976634979,"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":0.4311999976634979,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.18549999594688416,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.065700002014637,"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/continuation","display_name":"Continuation","score":0.6553999781608582},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6373000144958496},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.5034000277519226},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.4724999964237213},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.4165000021457672},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4068000018596649},{"id":"https://openalex.org/keywords/trigonometric-polynomial","display_name":"Trigonometric polynomial","score":0.3871000111103058},{"id":"https://openalex.org/keywords/analytic-continuation","display_name":"Analytic continuation","score":0.384799987077713},{"id":"https://openalex.org/keywords/log-sum-inequality","display_name":"Log sum inequality","score":0.3790999948978424}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8227999806404114},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.6553999781608582},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6373000144958496},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.5034000277519226},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.4724999964237213},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.4165000021457672},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4068000018596649},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3926999866962433},{"id":"https://openalex.org/C156760230","wikidata":"https://www.wikidata.org/wiki/Q1969650","display_name":"Trigonometric polynomial","level":3,"score":0.3871000111103058},{"id":"https://openalex.org/C151602998","wikidata":"https://www.wikidata.org/wiki/Q485287","display_name":"Analytic continuation","level":2,"score":0.384799987077713},{"id":"https://openalex.org/C46979015","wikidata":"https://www.wikidata.org/wiki/Q6666859","display_name":"Log sum inequality","level":3,"score":0.3790999948978424},{"id":"https://openalex.org/C126087398","wikidata":"https://www.wikidata.org/wiki/Q1149189","display_name":"Rearrangement inequality","level":4,"score":0.3686999976634979},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3467000126838684},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.33629998564720154},{"id":"https://openalex.org/C206399364","wikidata":"https://www.wikidata.org/wiki/Q3154001","display_name":"Kantorovich inequality","level":4,"score":0.3310000002384186},{"id":"https://openalex.org/C68827188","wikidata":"https://www.wikidata.org/wiki/Q674533","display_name":"Inverse trigonometric functions","level":2,"score":0.32350000739097595},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.3188999891281128},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3151000142097473},{"id":"https://openalex.org/C184701930","wikidata":"https://www.wikidata.org/wiki/Q190546","display_name":"Cauchy\u2013Schwarz inequality","level":3,"score":0.3138999938964844},{"id":"https://openalex.org/C205979905","wikidata":"https://www.wikidata.org/wiki/Q215084","display_name":"Analytic function","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.29739999771118164},{"id":"https://openalex.org/C91558832","wikidata":"https://www.wikidata.org/wiki/Q731894","display_name":"H\u00f6lder's inequality","level":4,"score":0.289000004529953},{"id":"https://openalex.org/C2777487392","wikidata":"https://www.wikidata.org/wiki/Q481201","display_name":"Absolute (philosophy)","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2784000039100647},{"id":"https://openalex.org/C188791865","wikidata":"https://www.wikidata.org/wiki/Q366730","display_name":"Ky Fan inequality","level":5,"score":0.2712000012397766},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2529999911785126}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00029890.2018.1436837","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1436837","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1710.01270","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.01270","pdf_url":"https://arxiv.org/pdf/1710.01270","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1710.01270","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.01270","pdf_url":"https://arxiv.org/pdf/1710.01270","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2011023754","https://openalex.org/W2045529763","https://openalex.org/W2244940379","https://openalex.org/W2324309502","https://openalex.org/W4246293990","https://openalex.org/W4247973014"],"related_works":[],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2],"the":[3,7,35],"absolute":[4],"value":[5],"of":[6,10,31,38],"nth":[8],"derivative":[9],"does":[11],"not":[12],"exceed":[13],"n!/(2n)!":[14],"for":[15],"all":[16],"x":[17],">":[18],"0":[19],"and":[20,26],"n":[21],"=":[22],"0,":[23],"1,":[24],"\u2026":[25],"obtain":[27],"a":[28],"natural":[29],"generalization":[30],"this":[32],"inequality":[33],"involving":[34],"analytic":[36],"continuation":[37],".":[39]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2017-10-20T00:00:00"}
