{"id":"https://openalex.org/W4319786230","doi":"https://doi.org/10.3390/sym15020463","title":"Equivalent Conditions of the Reverse Hardy-Type Integral Inequalities","display_name":"Equivalent Conditions of the Reverse Hardy-Type Integral Inequalities","publication_year":2023,"publication_date":"2023-02-09","ids":{"openalex":"https://openalex.org/W4319786230","doi":"https://doi.org/10.3390/sym15020463"},"language":"en","primary_location":{"id":"doi:10.3390/sym15020463","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15020463","pdf_url":"https://www.mdpi.com/2073-8994/15/2/463/pdf?version=1675927903","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/2/463/pdf?version=1675927903","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/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/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","RU","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","Institute for Advanced Study, Program in Interdisciplinary Studies, 1 Einstein Dr, Princeton, NJ 08540, USA","Moscow Institute of Physics and Technology, Institutskiy per, d. 9, Dolgoprudny 141700, Russia"],"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":"Institute for Advanced Study, Program in Interdisciplinary Studies, 1 Einstein Dr, Princeton, NJ 08540, USA","institution_ids":["https://openalex.org/I40036882"]},{"raw_affiliation_string":"Moscow Institute of Physics and Technology, Institutskiy per, d. 9, Dolgoprudny 141700, Russia","institution_ids":["https://openalex.org/I153845743"]}]},{"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"]},{"id":"https://openalex.org/I201106796","display_name":"Buryat State University","ror":"https://ror.org/04rfsd440","country_code":"RU","type":"education","lineage":["https://openalex.org/I201106796"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Andrei Raigorodskii","raw_affiliation_strings":["Caucasus Mathematical Center, Adyghe State University, ul. Pervomayskaya, 208, Maykop 385000, Russia","Institute of Mathematics and Computer Science, Buryat State University, 24a Smolin St., Ulan-Ude 670000, Russia","Moscow Institute of Physics and Technology, Institutskiy per, d. 9, Dolgoprudny 141700, Russia","The Department of Statistics and Random Processes of the Mechanics and Mathematics Faculty of Lomonosov, Moscow State University, Leninskie Gory, 1, Moscow 119991, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caucasus Mathematical Center, Adyghe State University, ul. Pervomayskaya, 208, Maykop 385000, Russia","institution_ids":["https://openalex.org/I135226738"]},{"raw_affiliation_string":"Institute of Mathematics and Computer Science, Buryat State University, 24a Smolin St., Ulan-Ude 670000, Russia","institution_ids":["https://openalex.org/I201106796"]},{"raw_affiliation_string":"Moscow Institute of Physics and Technology, Institutskiy per, d. 9, Dolgoprudny 141700, Russia","institution_ids":["https://openalex.org/I153845743"]},{"raw_affiliation_string":"The Department of Statistics and Random Processes of the Mechanics and Mathematics Faculty of Lomonosov, Moscow State University, Leninskie Gory, 1, Moscow 119991, Russia","institution_ids":["https://openalex.org/I19880235"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050297643"],"corresponding_institution_ids":["https://openalex.org/I153845743","https://openalex.org/I24897511","https://openalex.org/I40036882"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02445575,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"2","first_page":"463","last_page":"463"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.991599977016449,"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":0.9631999731063843,"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":0.7820442914962769},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6260924339294434},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5920892953872681},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.578022301197052},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.5495107769966125},{"id":"https://openalex.org/keywords/integral-transform","display_name":"Integral transform","score":0.4358958899974823},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43121036887168884},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39739111065864563},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3248657286167145},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3009905219078064},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12857139110565186}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7820442914962769},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6260924339294434},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5920892953872681},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.578022301197052},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5495107769966125},{"id":"https://openalex.org/C200052193","wikidata":"https://www.wikidata.org/wiki/Q877802","display_name":"Integral transform","level":2,"score":0.4358958899974823},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43121036887168884},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39739111065864563},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3248657286167145},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3009905219078064},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12857139110565186},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15020463","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15020463","pdf_url":"https://www.mdpi.com/2073-8994/15/2/463/pdf?version=1675927903","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b67591fd7f7d45a6b7211f2f2283cdb2","is_oa":false,"landing_page_url":"https://doaj.org/article/b67591fd7f7d45a6b7211f2f2283cdb2","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 2, p 463 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/2/463/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15020463","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15020463","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15020463","pdf_url":"https://www.mdpi.com/2073-8994/15/2/463/pdf?version=1675927903","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7099999785423279,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4319786230.pdf"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1969629913","https://openalex.org/W1981427948","https://openalex.org/W2017761485","https://openalex.org/W2048788200","https://openalex.org/W2163643881","https://openalex.org/W2180798018","https://openalex.org/W2189472879","https://openalex.org/W2319572282","https://openalex.org/W2349621305","https://openalex.org/W2367564984","https://openalex.org/W2387587402","https://openalex.org/W2606228013","https://openalex.org/W2624394760","https://openalex.org/W2782779200","https://openalex.org/W2803422079","https://openalex.org/W3030069265","https://openalex.org/W3034446510","https://openalex.org/W3048505927","https://openalex.org/W3126057716","https://openalex.org/W3164147717","https://openalex.org/W3171396983","https://openalex.org/W3171924721","https://openalex.org/W6686974087","https://openalex.org/W6736775008","https://openalex.org/W6782380291","https://openalex.org/W6991537132"],"related_works":["https://openalex.org/W1598955744","https://openalex.org/W4285167822","https://openalex.org/W2951710344","https://openalex.org/W2204136089","https://openalex.org/W1917349875","https://openalex.org/W2144602163","https://openalex.org/W4384111961","https://openalex.org/W2127985649","https://openalex.org/W4249202279","https://openalex.org/W2157039219"],"abstract_inverted_index":{"Hardy-type":[0,55,72],"integral":[1,56,73],"inequalities":[2,57,74],"play":[3],"a":[4,59,76],"prominent":[5],"role":[6],"in":[7,16,25,82],"the":[8,26,83],"study":[9,27],"of":[10,28,38,50,53,67,70,85],"analytic":[11],"inequalities,":[12],"which":[13],"are":[14,80],"essential":[15],"mathematical":[17],"analysis":[18,40],"and":[19,30,41],"its":[20],"various":[21],"applications,":[22],"such":[23],"as":[24],"symmetry":[29],"asymmetry":[31],"phenomena.":[32],"In":[33],"this":[34],"paper,":[35],"employing":[36],"methods":[37],"real":[39],"using":[42],"weight":[43],"functions,":[44],"we":[45],"investigate":[46],"some":[47],"equivalent":[48,65],"conditions":[49,66],"two":[51,68],"kinds":[52,69],"reverse":[54,71],"with":[58,75],"particular":[60,77],"non-homogeneous":[61],"kernel.":[62],"A":[63],"few":[64],"homogeneous":[78],"kernel":[79],"deduced":[81],"form":[84],"applications.":[86]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}