{"id":"https://openalex.org/W4383878394","doi":"https://doi.org/10.3390/axioms12070677","title":"An Equivalent Form Related to a Hilbert-Type Integral Inequality","display_name":"An Equivalent Form Related to a Hilbert-Type Integral Inequality","publication_year":2023,"publication_date":"2023-07-10","ids":{"openalex":"https://openalex.org/W4383878394","doi":"https://doi.org/10.3390/axioms12070677"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12070677","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070677","pdf_url":"https://www.mdpi.com/2075-1680/12/7/677/pdf?version=1688984534","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/2075-1680/12/7/677/pdf?version=1688984534","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050297643","display_name":"Michael Th. Rassias","orcid":"https://orcid.org/0000-0001-8395-8748"},"institutions":[{"id":"https://openalex.org/I24897511","display_name":"Hellenic Military Academy","ror":"https://ror.org/01esc8r67","country_code":"GR","type":"education","lineage":["https://openalex.org/I24897511"]},{"id":"https://openalex.org/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]}],"countries":["GR","US"],"is_corresponding":true,"raw_author_name":"Michael Th. Rassias","raw_affiliation_strings":["Department of Mathematics and Engineering Sciences, Hellenic Military Academy, 16673 Vari Attikis, Greece","Program in Interdisciplinary Studies, Institute for Advanced Study, 1 Einstein Dr, Princeton, NJ 08540, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Engineering Sciences, Hellenic Military Academy, 16673 Vari Attikis, Greece","institution_ids":["https://openalex.org/I24897511"]},{"raw_affiliation_string":"Program in Interdisciplinary Studies, Institute for Advanced Study, 1 Einstein Dr, Princeton, NJ 08540, USA","institution_ids":["https://openalex.org/I40036882"]}]},{"author_position":"middle","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":false,"raw_author_name":"Bicheng Yang","raw_affiliation_strings":["Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department 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/A5083898614","display_name":"\u0410. \u041c. \u0420\u0430\u0439\u0433\u043e\u0440\u043e\u0434\u0441\u043a\u0438\u0439","orcid":"https://orcid.org/0000-0001-8614-9612"},"institutions":[{"id":"https://openalex.org/I135226738","display_name":"Adyghe State University","ror":"https://ror.org/00tf0yk25","country_code":"RU","type":"education","lineage":["https://openalex.org/I135226738"]},{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]},{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Andrei Raigorodskii","raw_affiliation_strings":["Caucasus Mathematical Center, Adyghe State University, 385000 Maykop, Russia","Department of Mechanics and Mathematics, Moscow State University, 119991 Moscow, Russia","Moscow Institute of Physics and Technology, Institutskiy per, d. 9, 141700 Dolgoprudny, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caucasus Mathematical Center, Adyghe State University, 385000 Maykop, Russia","institution_ids":["https://openalex.org/I135226738"]},{"raw_affiliation_string":"Department of Mechanics and Mathematics, Moscow State University, 119991 Moscow, Russia","institution_ids":["https://openalex.org/I19880235"]},{"raw_affiliation_string":"Moscow Institute of Physics and Technology, Institutskiy per, d. 9, 141700 Dolgoprudny, Russia","institution_ids":["https://openalex.org/I153845743"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050297643"],"corresponding_institution_ids":["https://openalex.org/I24897511","https://openalex.org/I40036882"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":3.0137,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.90994914,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"12","issue":"7","first_page":"677","last_page":"677"},"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":0.9753000140190125,"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":0.9588000178337097,"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":0.7646251916885376},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.617722749710083},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5897002220153809},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5107216835021973},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.5091070532798767},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5076104402542114},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4865473806858063},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.44446611404418945},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4285407066345215},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3892000615596771},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.3439735174179077},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13057342171669006},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11550673842430115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7646251916885376},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.617722749710083},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5897002220153809},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5107216835021973},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5091070532798767},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5076104402542114},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4865473806858063},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.44446611404418945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4285407066345215},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3892000615596771},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.3439735174179077},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13057342171669006},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11550673842430115},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12070677","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070677","pdf_url":"https://www.mdpi.com/2075-1680/12/7/677/pdf?version=1688984534","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:78db8b75ed6d4008b01e7952e4f4fd3a","is_oa":true,"landing_page_url":"https://doaj.org/article/78db8b75ed6d4008b01e7952e4f4fd3a","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 7, p 677 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/7/677/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12070677","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; Volume 12; Issue 7; Pages: 677","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12070677","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070677","pdf_url":"https://www.mdpi.com/2075-1680/12/7/677/pdf?version=1688984534","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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6100000143051147}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4383878394.pdf"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W104279468","https://openalex.org/W1981427948","https://openalex.org/W2017761485","https://openalex.org/W2163643881","https://openalex.org/W2189472879","https://openalex.org/W2319572282","https://openalex.org/W2349621305","https://openalex.org/W2367564984","https://openalex.org/W2387587402","https://openalex.org/W2782779200","https://openalex.org/W3048505927","https://openalex.org/W3092708982","https://openalex.org/W3164147717","https://openalex.org/W3171396983","https://openalex.org/W4280583794","https://openalex.org/W4296503233","https://openalex.org/W6686974087","https://openalex.org/W6782380291","https://openalex.org/W6991537132"],"related_works":["https://openalex.org/W2065805792","https://openalex.org/W4285290579","https://openalex.org/W149320920","https://openalex.org/W3125885229","https://openalex.org/W4234882900","https://openalex.org/W1527525543","https://openalex.org/W2370512383","https://openalex.org/W2896570485","https://openalex.org/W1835315728","https://openalex.org/W2962818398"],"abstract_inverted_index":{"In":[0],"the":[1,28],"present":[2],"paper,":[3],"we":[4],"establish":[5],"an":[6],"equivalent":[7],"form":[8],"related":[9],"to":[10],"a":[11,16,20],"Hilbert-type":[12],"integral":[13],"inequality":[14],"with":[15],"non-homogeneous":[17],"kernel":[18,32],"and":[19],"best":[21],"possible":[22],"constant":[23],"factor.":[24],"We":[25],"also":[26],"consider":[27],"case":[29],"of":[30],"homogeneous":[31],"as":[33,35],"well":[34],"certain":[36],"operator":[37],"expressions.":[38]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2023-07-12T00:00:00"}
