{"id":"https://openalex.org/W2049371465","doi":"https://doi.org/10.1155/2008/297508","title":"On New Extensions of Hilbert\u2032s Integral Inequality","display_name":"On New Extensions of Hilbert\u2032s Integral Inequality","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2049371465","doi":"https://doi.org/10.1155/2008/297508","mag":"2049371465"},"language":"en","primary_location":{"id":"doi:10.1155/2008/297508","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2008/297508","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2008/297508.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","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/ijmms/2008/297508.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101860357","display_name":"HE Le-ping","orcid":"https://orcid.org/0000-0001-6671-9665"},"institutions":[{"id":"https://openalex.org/I144581915","display_name":"Jishou University","ror":"https://ror.org/056szk247","country_code":"CN","type":"education","lineage":["https://openalex.org/I144581915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"He Leping","raw_affiliation_strings":["Department of Mathematics and Applied Mathematics, College of Mathematics and Computer Science, Jishou University, Jishou Hunan 416000, China","Department of Mathematics and Applied Mathematics, College of Mathematics and Computer Science, Jishou University, Jishou Hunan 416000"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, College of Mathematics and Computer Science, Jishou University, Jishou Hunan 416000, China","institution_ids":["https://openalex.org/I144581915"]},{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, College of Mathematics and Computer Science, Jishou University, Jishou Hunan 416000","institution_ids":["https://openalex.org/I144581915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079617879","display_name":"Gao Mingzhe","orcid":null},"institutions":[{"id":"https://openalex.org/I144581915","display_name":"Jishou University","ror":"https://ror.org/056szk247","country_code":"CN","type":"education","lineage":["https://openalex.org/I144581915"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Gao Mingzhe","raw_affiliation_strings":["Department of Mathematics and Computer Science, Normal College of Jishou University, Jishou Hunan 416000, China","Department of Mathematics and Computer Science, Normal College of Jishou University, Jishou Hunan 416000"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Normal College of Jishou University, Jishou Hunan 416000, China","institution_ids":["https://openalex.org/I144581915"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, Normal College of Jishou University, Jishou Hunan 416000","institution_ids":["https://openalex.org/I144581915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101658389","display_name":"Zhou Yu","orcid":"https://orcid.org/0000-0002-9718-2466"},"institutions":[{"id":"https://openalex.org/I144581915","display_name":"Jishou University","ror":"https://ror.org/056szk247","country_code":"CN","type":"education","lineage":["https://openalex.org/I144581915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhou Yu","raw_affiliation_strings":["Department of Mathematics and Computer Science, Normal College of Jishou University, Jishou Hunan 416000, China","Department of Mathematics and Computer Science, Normal College of Jishou University, Jishou Hunan 416000"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Normal College of Jishou University, Jishou Hunan 416000, China","institution_ids":["https://openalex.org/I144581915"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, Normal College of Jishou University, Jishou Hunan 416000","institution_ids":["https://openalex.org/I144581915"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079617879"],"corresponding_institution_ids":["https://openalex.org/I144581915"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":2.152,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.8591925,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2008","issue":"1","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":0.9997000098228455,"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":0.9997000098228455,"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/T12504","display_name":"Mathematics and Applications","score":0.9553999900817871,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9179999828338623,"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/mathematics","display_name":"Mathematics","score":0.9087275862693787},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.7265629768371582},{"id":"https://openalex.org/keywords/rearrangement-inequality","display_name":"Rearrangement inequality","score":0.5724900960922241},{"id":"https://openalex.org/keywords/h\u00f6lders-inequality","display_name":"H\u00f6lder's inequality","score":0.5501627326011658},{"id":"https://openalex.org/keywords/kantorovich-inequality","display_name":"Kantorovich inequality","score":0.527875542640686},{"id":"https://openalex.org/keywords/log-sum-inequality","display_name":"Log sum inequality","score":0.5112519264221191},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.49715355038642883},{"id":"https://openalex.org/keywords/weight-function","display_name":"Weight function","score":0.48314613103866577},{"id":"https://openalex.org/keywords/bessels-inequality","display_name":"Bessel's inequality","score":0.43458807468414307},{"id":"https://openalex.org/keywords/gronwalls-inequality","display_name":"Gronwall's inequality","score":0.4104098677635193},{"id":"https://openalex.org/keywords/linear-inequality","display_name":"Linear inequality","score":0.39744043350219727},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3853999674320221}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9087275862693787},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.7265629768371582},{"id":"https://openalex.org/C126087398","wikidata":"https://www.wikidata.org/wiki/Q1149189","display_name":"Rearrangement inequality","level":4,"score":0.5724900960922241},{"id":"https://openalex.org/C91558832","wikidata":"https://www.wikidata.org/wiki/Q731894","display_name":"H\u00f6lder's inequality","level":4,"score":0.5501627326011658},{"id":"https://openalex.org/C206399364","wikidata":"https://www.wikidata.org/wiki/Q3154001","display_name":"Kantorovich inequality","level":4,"score":0.527875542640686},{"id":"https://openalex.org/C46979015","wikidata":"https://www.wikidata.org/wiki/Q6666859","display_name":"Log sum inequality","level":3,"score":0.5112519264221191},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49715355038642883},{"id":"https://openalex.org/C134466208","wikidata":"https://www.wikidata.org/wiki/Q1520657","display_name":"Weight function","level":2,"score":0.48314613103866577},{"id":"https://openalex.org/C59037737","wikidata":"https://www.wikidata.org/wiki/Q794042","display_name":"Bessel's inequality","level":5,"score":0.43458807468414307},{"id":"https://openalex.org/C37608338","wikidata":"https://www.wikidata.org/wiki/Q510733","display_name":"Gronwall's inequality","level":3,"score":0.4104098677635193},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.39744043350219727},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3853999674320221}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2008/297508","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2008/297508","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2008/297508.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:297508","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2008/297508.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:4f0420011b3841a18ca4ce873837dc93","is_oa":true,"landing_page_url":"https://doaj.org/article/4f0420011b3841a18ca4ce873837dc93","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2008 (2008)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2008/297508","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2008/297508","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2008/297508.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5699999928474426,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2049371465.pdf","grobid_xml":"https://content.openalex.org/works/W2049371465.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1975435572","https://openalex.org/W1994518041","https://openalex.org/W2136506999","https://openalex.org/W2157005274","https://openalex.org/W2390073620","https://openalex.org/W3008609509"],"related_works":["https://openalex.org/W2163968995","https://openalex.org/W2135005783","https://openalex.org/W1746349491","https://openalex.org/W1992927286","https://openalex.org/W4300650764","https://openalex.org/W2327838734","https://openalex.org/W2165910847","https://openalex.org/W2949723170","https://openalex.org/W1998520836","https://openalex.org/W2187892923"],"abstract_inverted_index":{"It":[0],"is":[1,39],"shown":[2],"that":[3],"some":[4,43],"new":[5,44],"extensions":[6,45],"of":[7,35,46],"Hilbert\u2032s":[8,36],"integral":[9,37],"inequality":[10,38,48,51],"with":[11],"parameter":[12],"\u03bb":[13,15,30],"(":[14],">":[16],"1/2)":[17],"can":[18],"be":[19],"established":[20],"by":[21],"introducing":[22],"a":[23,33],"proper":[24],"weight":[25],"function.":[26],"In":[27],"particular,":[28],"when":[29],"=":[31],"1,":[32],"refinement":[34],"obtained.":[40],"As":[41],"applications,":[42],"Widder\u2032s":[47],"and":[49],"Hardy\u2010Littlewood\u2032s":[50],"are":[52],"given.":[53]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}