{"id":"https://openalex.org/W4386600784","doi":"https://doi.org/10.3390/axioms12090871","title":"An Extended Hilbert-Type Inequality with Two Internal Variables Involving One Partial Sums","display_name":"An Extended Hilbert-Type Inequality with Two Internal Variables Involving One Partial Sums","publication_year":2023,"publication_date":"2023-09-10","ids":{"openalex":"https://openalex.org/W4386600784","doi":"https://doi.org/10.3390/axioms12090871"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12090871","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12090871","pdf_url":"https://www.mdpi.com/2075-1680/12/9/871/pdf?version=1694329722","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/9/871/pdf?version=1694329722","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Aizhen Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I201459984","display_name":"Guangdong University Of Finances and Economics","ror":"https://ror.org/0459pv085","country_code":"CN","type":"education","lineage":["https://openalex.org/I201459984"]},{"id":"https://openalex.org/I32246829","display_name":"Guangdong University of Education","ror":"https://ror.org/0574der91","country_code":"CN","type":"education","lineage":["https://openalex.org/I32246829"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Aizhen Wang","raw_affiliation_strings":["School of Mathematics, Guangdong University of Education, Guangzhou 510303, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Guangdong University of Education, Guangzhou 510303, China","institution_ids":["https://openalex.org/I201459984","https://openalex.org/I32246829"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100674358","display_name":"Bicheng Yang","orcid":"https://orcid.org/0000-0002-9417-3310"},"institutions":[{"id":"https://openalex.org/I201459984","display_name":"Guangdong University Of Finances and Economics","ror":"https://ror.org/0459pv085","country_code":"CN","type":"education","lineage":["https://openalex.org/I201459984"]},{"id":"https://openalex.org/I32246829","display_name":"Guangdong University of Education","ror":"https://ror.org/0574der91","country_code":"CN","type":"education","lineage":["https://openalex.org/I32246829"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bicheng Yang","raw_affiliation_strings":["School of Mathematics, Guangdong University of Education, Guangzhou 510303, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Guangdong University of Education, Guangzhou 510303, China","institution_ids":["https://openalex.org/I201459984","https://openalex.org/I32246829"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100674358"],"corresponding_institution_ids":["https://openalex.org/I201459984","https://openalex.org/I32246829"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.0046,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.731353,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"12","issue":"9","first_page":"871","last_page":"871"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T12508","display_name":"Functional Equations Stability Results","score":0.9564999938011169,"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/T11822","display_name":"Analytic and geometric function theory","score":0.9426000118255615,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7892820835113525},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.7147913575172424},{"id":"https://openalex.org/keywords/log-sum-inequality","display_name":"Log sum inequality","score":0.565578281879425},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.549699604511261},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5458968877792358},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4906967878341675},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4842352569103241},{"id":"https://openalex.org/keywords/kantorovich-inequality","display_name":"Kantorovich inequality","score":0.4718886613845825},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4581020176410675},{"id":"https://openalex.org/keywords/rearrangement-inequality","display_name":"Rearrangement inequality","score":0.4456930458545685},{"id":"https://openalex.org/keywords/bernoullis-inequality","display_name":"Bernoulli's inequality","score":0.4415532946586609},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.41914495825767517},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3449791967868805},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33626699447631836},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3295602798461914},{"id":"https://openalex.org/keywords/linear-inequality","display_name":"Linear inequality","score":0.28584596514701843},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09060534834861755}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7892820835113525},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.7147913575172424},{"id":"https://openalex.org/C46979015","wikidata":"https://www.wikidata.org/wiki/Q6666859","display_name":"Log sum inequality","level":3,"score":0.565578281879425},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.549699604511261},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5458968877792358},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4906967878341675},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4842352569103241},{"id":"https://openalex.org/C206399364","wikidata":"https://www.wikidata.org/wiki/Q3154001","display_name":"Kantorovich inequality","level":4,"score":0.4718886613845825},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4581020176410675},{"id":"https://openalex.org/C126087398","wikidata":"https://www.wikidata.org/wiki/Q1149189","display_name":"Rearrangement inequality","level":4,"score":0.4456930458545685},{"id":"https://openalex.org/C177180624","wikidata":"https://www.wikidata.org/wiki/Q728662","display_name":"Bernoulli's inequality","level":5,"score":0.4415532946586609},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.41914495825767517},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3449791967868805},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33626699447631836},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3295602798461914},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.28584596514701843},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09060534834861755},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12090871","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12090871","pdf_url":"https://www.mdpi.com/2075-1680/12/9/871/pdf?version=1694329722","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:525794729d7d4613af00d0ef67e525f0","is_oa":true,"landing_page_url":"https://doaj.org/article/525794729d7d4613af00d0ef67e525f0","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":"Axioms, Vol 12, Iss 9, p 871 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/9/871/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12090871","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12090871","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12090871","pdf_url":"https://www.mdpi.com/2075-1680/12/9/871/pdf?version=1694329722","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.6000000238418579,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G764509512","display_name":null,"funder_award_id":"61772140","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386600784.pdf","grobid_xml":"https://content.openalex.org/works/W4386600784.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W104279468","https://openalex.org/W641756309","https://openalex.org/W1031006317","https://openalex.org/W2043909583","https://openalex.org/W2077945704","https://openalex.org/W2139870747","https://openalex.org/W2213931986","https://openalex.org/W2328344058","https://openalex.org/W2333537478","https://openalex.org/W2367564984","https://openalex.org/W2778511222","https://openalex.org/W2889151004","https://openalex.org/W2893693984","https://openalex.org/W2947236134","https://openalex.org/W3048505927","https://openalex.org/W3092708982","https://openalex.org/W3164147717","https://openalex.org/W3171396983","https://openalex.org/W4200023079","https://openalex.org/W4383910999","https://openalex.org/W4385200393","https://openalex.org/W6702215255","https://openalex.org/W6753787393","https://openalex.org/W6782380291","https://openalex.org/W6991537132"],"related_works":["https://openalex.org/W2367379155","https://openalex.org/W2358412019","https://openalex.org/W2375563811","https://openalex.org/W2044647149","https://openalex.org/W2348057472","https://openalex.org/W2352680697","https://openalex.org/W2163968995","https://openalex.org/W2950086839","https://openalex.org/W3157790919","https://openalex.org/W2949723170"],"abstract_inverted_index":{"By":[0],"the":[1,4,43,53,56,66],"use":[2],"of":[3,6,17,32,42],"techniques":[5],"analysis":[7],"and":[8],"some":[9],"useful":[10],"formulas,":[11],"we":[12],"give":[13],"a":[14,30,33,38,62],"new":[15],"extension":[16],"Hilbert-type":[18],"inequality":[19],"with":[20,65],"two":[21],"internal":[22],"variables":[23],"involving":[24],"one":[25],"partial":[26],"sums,":[27],"which":[28],"is":[29],"refinement":[31],"published":[34],"inequality.":[35],"We":[36,51],"provide":[37],"few":[39,63],"equivalent":[40,54],"conditions":[41],"best":[44],"possible":[45],"constant":[46],"related":[47],"to":[48],"multi":[49],"parameters.":[50],"obtain":[52],"inequalities,":[55],"operator":[57],"expressions":[58],"as":[59,61,69],"well":[60],"inequalities":[64],"particular":[67],"parameters":[68],"applications.":[70]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}