{"id":"https://openalex.org/W4366089624","doi":"https://doi.org/10.3390/sym15040925","title":"Some Refinements of the Tensorial Inequalities in Hilbert Spaces","display_name":"Some Refinements of the Tensorial Inequalities in Hilbert Spaces","publication_year":2023,"publication_date":"2023-04-16","ids":{"openalex":"https://openalex.org/W4366089624","doi":"https://doi.org/10.3390/sym15040925"},"language":"en","primary_location":{"id":"doi:10.3390/sym15040925","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040925","pdf_url":"https://www.mdpi.com/2073-8994/15/4/925/pdf?version=1681634607","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/2073-8994/15/4/925/pdf?version=1681634607","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046160337","display_name":"Vuk Stojiljkovi\u0107","orcid":"https://orcid.org/0000-0002-4244-4342"},"institutions":[{"id":"https://openalex.org/I170726198","display_name":"University of Novi Sad","ror":"https://ror.org/00xa57a59","country_code":"RS","type":"education","lineage":["https://openalex.org/I170726198"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Vuk Stojiljkovi\u0107","raw_affiliation_strings":["Faculty of Science, University of Novi Sad, Trg Dositeja Obradovi\u0107a 3, 21000 Novi Sad, Serbia"],"raw_orcid":"https://orcid.org/0000-0002-4244-4342","affiliations":[{"raw_affiliation_string":"Faculty of Science, University of Novi Sad, Trg Dositeja Obradovi\u0107a 3, 21000 Novi Sad, Serbia","institution_ids":["https://openalex.org/I170726198"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004471107","display_name":"Rajagopalan Ramaswamy","orcid":"https://orcid.org/0000-0001-9027-0810"},"institutions":[{"id":"https://openalex.org/I142608572","display_name":"Prince Sattam Bin Abdulaziz University","ror":"https://ror.org/04jt46d36","country_code":"SA","type":"education","lineage":["https://openalex.org/I142608572"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Rajagopalan Ramaswamy","raw_affiliation_strings":["Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz Univeristy, Al-Kharj 16278, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-9027-0810","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz Univeristy, Al-Kharj 16278, Saudi Arabia","institution_ids":["https://openalex.org/I142608572"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037884522","display_name":"Ola A. Ashour Abdelnaby","orcid":"https://orcid.org/0000-0003-1687-3212"},"institutions":[{"id":"https://openalex.org/I142608572","display_name":"Prince Sattam Bin Abdulaziz University","ror":"https://ror.org/04jt46d36","country_code":"SA","type":"education","lineage":["https://openalex.org/I142608572"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ola A. Ashour Abdelnaby","raw_affiliation_strings":["Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz Univeristy, Al-Kharj 16278, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-1687-3212","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz Univeristy, Al-Kharj 16278, Saudi Arabia","institution_ids":["https://openalex.org/I142608572"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032620709","display_name":"Stojan Radenovi\u0107","orcid":"https://orcid.org/0000-0001-8254-6688"},"institutions":[{"id":"https://openalex.org/I4068193","display_name":"University of Belgrade","ror":"https://ror.org/02qsmb048","country_code":"RS","type":"education","lineage":["https://openalex.org/I4068193"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Stojan Radenovi\u0107","raw_affiliation_strings":["Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia"],"raw_orcid":"https://orcid.org/0000-0001-8254-6688","affiliations":[{"raw_affiliation_string":"Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia","institution_ids":["https://openalex.org/I4068193"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004471107"],"corresponding_institution_ids":["https://openalex.org/I142608572"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":5.1006,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.96087502,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"15","issue":"4","first_page":"925","last_page":"925"},"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":0.964900016784668,"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":0.9340999722480774,"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/mathematics","display_name":"Mathematics","score":0.8056567907333374},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6475170254707336},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.617725670337677},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5920250415802002},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.5879454016685486},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.54767906665802},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5270436406135559},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4968729317188263},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.45243197679519653},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4519205093383789},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32816874980926514},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32250556349754333},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0841120183467865},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06720450520515442}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8056567907333374},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6475170254707336},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.617725670337677},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5920250415802002},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.5879454016685486},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.54767906665802},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5270436406135559},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4968729317188263},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.45243197679519653},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4519205093383789},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32816874980926514},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32250556349754333},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0841120183467865},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06720450520515442},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15040925","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040925","pdf_url":"https://www.mdpi.com/2073-8994/15/4/925/pdf?version=1681634607","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:73b20390343c4153b7a357f314ae3ac6","is_oa":false,"landing_page_url":"https://doaj.org/article/73b20390343c4153b7a357f314ae3ac6","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 4, p 925 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/4/925/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15040925","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/sym15040925","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040925","pdf_url":"https://www.mdpi.com/2073-8994/15/4/925/pdf?version=1681634607","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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.6399999856948853}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4366089624.pdf"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1691106616","https://openalex.org/W1973596747","https://openalex.org/W2042793560","https://openalex.org/W2067176773","https://openalex.org/W2068963497","https://openalex.org/W2097240153","https://openalex.org/W2156288750","https://openalex.org/W2187850520","https://openalex.org/W2487728874","https://openalex.org/W2519050643","https://openalex.org/W3132844534","https://openalex.org/W4220737027","https://openalex.org/W4246293990","https://openalex.org/W4283777097","https://openalex.org/W4285094224","https://openalex.org/W4292476186","https://openalex.org/W4294081341","https://openalex.org/W4295797457","https://openalex.org/W4297236595","https://openalex.org/W4307732528","https://openalex.org/W4309740981","https://openalex.org/W4311981027","https://openalex.org/W4317738854","https://openalex.org/W4318426932","https://openalex.org/W4319598608","https://openalex.org/W4388425301","https://openalex.org/W6687134351","https://openalex.org/W6791606018"],"related_works":["https://openalex.org/W4396753818","https://openalex.org/W4294618985","https://openalex.org/W2518252082","https://openalex.org/W2364547801","https://openalex.org/W2788930696","https://openalex.org/W4301016436","https://openalex.org/W4293867722","https://openalex.org/W4297791001","https://openalex.org/W4206205240","https://openalex.org/W2277657541"],"abstract_inverted_index":{"Hermite\u2013Hadamard":[0,22],"inequalities":[1,39,44,64],"and":[2,75,82,99],"their":[3],"refinements":[4,19],"have":[5,69],"been":[6,70],"investigated":[7],"for":[8,27,65],"a":[9,104],"long":[10],"period":[11],"of":[12,20,24,31,61,92],"time.":[13],"In":[14],"this":[15],"paper,":[16],"we":[17],"obtained":[18,38,43,63],"the":[21,28,41,57,62,73,80,89,93,97],"inequality":[23],"tensorial":[25],"type":[26],"convex":[29,67],"functions":[30,68],"self-adjoint":[32],"operators":[33],"in":[34,72,79,88],"Hilbert":[35],"spaces.":[36],"The":[37,59],"generalize":[40],"previously":[42],"by":[45,103],"Dragomir.":[46],"We":[47],"also":[48],"provide":[49],"useful":[50],"Lemmas":[51],"which":[52],"enabled":[53],"us":[54],"to":[55],"obtain":[56],"results.":[58],"examples":[60],"specific":[66],"given":[71],"example":[74],"consequences":[76],"section.":[77],"Symmetry":[78],"upper":[81,98],"lower":[83,100],"bounds":[84,101],"can":[85],"be":[86],"seen":[87],"last":[90],"Theorem":[91],"paper":[94],"given,":[95],"as":[96],"differ":[102],"constant.":[105]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":3}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}