{"id":"https://openalex.org/W4383906326","doi":"https://doi.org/10.1142/s0219691323500364","title":"A kind of sharp Wirtinger inequalities","display_name":"A kind of sharp Wirtinger inequalities","publication_year":2023,"publication_date":"2023-07-11","ids":{"openalex":"https://openalex.org/W4383906326","doi":"https://doi.org/10.1142/s0219691323500364"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691323500364","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691323500364","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031300526","display_name":"Guiqiao Xu","orcid":"https://orcid.org/0000-0003-1448-2963"},"institutions":[{"id":"https://openalex.org/I15062923","display_name":"Tianjin Normal University","ror":"https://ror.org/05x2td559","country_code":"CN","type":"education","lineage":["https://openalex.org/I15062923"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guiqiao Xu","raw_affiliation_strings":["School of Mathematical Science, Tianjin Normal University, No. 393, Extension of Bin Shui West Road, Tianjin 300387, P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-1448-2963","affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Tianjin Normal University, No. 393, Extension of Bin Shui West Road, Tianjin 300387, P. R. China","institution_ids":["https://openalex.org/I15062923"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106716496","display_name":"Yongping Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongping Liu","raw_affiliation_strings":["Department of Mathematics, Beijing Normal University, No. 19, Xinjiekouwai St Beijing 100875, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Beijing Normal University, No. 19, Xinjiekouwai St Beijing 100875, P. R. China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5092446737","display_name":"Dandan Guo","orcid":null},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dandan Guo","raw_affiliation_strings":["Department of Mathematics, Beijing Normal University, No. 19, Xinjiekouwai St Beijing 100875, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Beijing Normal University, No. 19, Xinjiekouwai St Beijing 100875, P. R. China","institution_ids":["https://openalex.org/I25254941"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12618297,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"01","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9987000226974487,"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":0.9987000226974487,"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":0.9958000183105469,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.5829599499702454},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32190847396850586},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1160036027431488}],"concepts":[{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5829599499702454},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32190847396850586},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1160036027431488}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219691323500364","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691323500364","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5699999928474426}],"awards":[{"id":"https://openalex.org/G1227297294","display_name":null,"funder_award_id":"11871006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8265203038","display_name":null,"funder_award_id":"11671271","funder_id":"https://openalex.org/F4320310121","funder_display_name":"Natural Science Foundation of Jilin Province"}],"funders":[{"id":"https://openalex.org/F4320310121","display_name":"Natural Science Foundation of Jilin Province","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1981787994","https://openalex.org/W2179221244","https://openalex.org/W2949468895","https://openalex.org/W3000826180"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"This":[0],"study":[1],"gives":[2],"a":[3,44,65,133],"kind":[4],"of":[5,55,64,73,81,92,99],"sharp":[6],"Wirtinger":[7],"inequalities":[8],"(Pizone":[9],"inequalities)":[10],"[Formula:":[11,15,21,28,40,56,74,93],"see":[12,16,22,29,41,57,75,94],"text]":[13,17,23,42,58,76,95],"where":[14],"with":[18],"at":[19],"least":[20],"zeros":[24],"(counting":[25],"multiplicity)":[26],"in":[27,114],"text].":[30],"First,":[31],"based":[32],"on":[33],"the":[34,53,60,71,79,82,90,97,110],"Hermite":[35],"(Lagrange)":[36],"interpolation,":[37],"we":[38,51,69,88],"express":[39],"as":[43],"Lagrange":[45],"type":[46],"(integral":[47],"type)":[48],"remainder.":[49],"Second,":[50],"refer":[52,89],"computation":[54,91],"to":[59,96,109],"maximum":[61],"value":[62],"problem":[63],"multivariate":[66,83],"function,":[67,136],"and":[68,107,122],"give":[70],"values":[72],"by":[77],"finding":[78],"solution":[80],"function":[84],"aforementioned.":[85],"At":[86],"last,":[87],"norm":[98],"an":[100],"integral":[101],"operator.":[102],"Our":[103],"results":[104,111],"are":[105],"corrections":[106],"extensions":[108],"that":[112],"appear":[113],"[J.":[115],"C.":[116],"Kuang,":[117],"Applied":[118],"Inequalities":[119],"(Shandong":[120],"Science":[121],"Technology":[123],"Press,":[124],"Jinan,":[125],"2004);":[126],"A.":[127],"Yu.":[128],"Levin,":[129],"Some":[130],"estimates":[131],"for":[132],"diff":[134],"erentiable":[135],"Dokl.":[137],"Akad.":[138],"Nauk":[139],"SSSR":[140],"138":[141],"(1961)":[142],"37-38":[143],"(in":[144],"Russian)].":[145]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
