{"id":"https://openalex.org/W4304184083","doi":"https://doi.org/10.3390/sym14102043","title":"Some New Generalizations of Reverse Hilbert-Type Inequalities via Supermultiplicative Functions","display_name":"Some New Generalizations of Reverse Hilbert-Type Inequalities via Supermultiplicative Functions","publication_year":2022,"publication_date":"2022-09-30","ids":{"openalex":"https://openalex.org/W4304184083","doi":"https://doi.org/10.3390/sym14102043"},"language":"en","primary_location":{"id":"doi:10.3390/sym14102043","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14102043","pdf_url":"https://www.mdpi.com/2073-8994/14/10/2043/pdf?version=1666666692","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/2073-8994/14/10/2043/pdf?version=1666666692","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004188579","display_name":"Haytham M. Rezk","orcid":"https://orcid.org/0000-0001-6782-7908"},"institutions":[{"id":"https://openalex.org/I184834183","display_name":"Al-Azhar University","ror":"https://ror.org/05fnp1145","country_code":"EG","type":"education","lineage":["https://openalex.org/I184834183"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Haytham M. Rezk","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt"],"raw_orcid":"https://orcid.org/0000-0001-6782-7908","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt","institution_ids":["https://openalex.org/I184834183"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079939262","display_name":"Ahmed I. Saied","orcid":null},"institutions":[{"id":"https://openalex.org/I207547235","display_name":"Benha University","ror":"https://ror.org/03tn5ee41","country_code":"EG","type":"education","lineage":["https://openalex.org/I207547235"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Ahmed I. Saied","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt","institution_ids":["https://openalex.org/I207547235"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002110465","display_name":"Ghada AlNemer","orcid":"https://orcid.org/0000-0002-2222-7973"},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ghada AlNemer","raw_affiliation_strings":["Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-2222-7973","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060547119","display_name":"Mohammed Zakarya","orcid":"https://orcid.org/0000-0003-4312-8330"},"institutions":[{"id":"https://openalex.org/I184834183","display_name":"Al-Azhar University","ror":"https://ror.org/05fnp1145","country_code":"EG","type":"education","lineage":["https://openalex.org/I184834183"]},{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["EG","SA"],"is_corresponding":false,"raw_author_name":"Mohammed Zakarya","raw_affiliation_strings":["Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia","Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt"],"raw_orcid":"https://orcid.org/0000-0003-4312-8330","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt","institution_ids":["https://openalex.org/I184834183"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5004188579"],"corresponding_institution_ids":["https://openalex.org/I184834183"],"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":0.16357786,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"10","first_page":"2043","last_page":"2043"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.998199999332428,"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":0.998199999332428,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9832000136375427,"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":0.964900016784668,"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/hilbert-space","display_name":"Hilbert space","score":0.6758905649185181},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6272283792495728},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5408115983009338},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.47587648034095764},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4508516490459442},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4431454837322235},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.4269979000091553},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4162341356277466},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4152206778526306},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24644744396209717}],"concepts":[{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6758905649185181},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6272283792495728},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5408115983009338},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.47587648034095764},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4508516490459442},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4431454837322235},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.4269979000091553},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4162341356277466},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4152206778526306},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24644744396209717},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14102043","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14102043","pdf_url":"https://www.mdpi.com/2073-8994/14/10/2043/pdf?version=1666666692","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:2f4e9837674f4ac4a9640f8d4f63c1a5","is_oa":true,"landing_page_url":"https://doaj.org/article/2f4e9837674f4ac4a9640f8d4f63c1a5","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":"Symmetry, Vol 14, Iss 10, p 2043 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/10/2043/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14102043","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/sym14102043","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14102043","pdf_url":"https://www.mdpi.com/2073-8994/14/10/2043/pdf?version=1666666692","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":0.6499999761581421,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G7384355510","display_name":null,"funder_award_id":"PNURSP2022R45","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"}],"funders":[{"id":"https://openalex.org/F4320322484","display_name":"Princess Nourah Bint Abdulrahman University","ror":"https://ror.org/05b0cyh02"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4304184083.pdf","grobid_xml":"https://content.openalex.org/works/W4304184083.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W271810198","https://openalex.org/W1522419168","https://openalex.org/W1551815804","https://openalex.org/W2089985530","https://openalex.org/W2346930633","https://openalex.org/W2379423647","https://openalex.org/W2761174678","https://openalex.org/W2790398604","https://openalex.org/W3013074447","https://openalex.org/W3080489491","https://openalex.org/W4200570605","https://openalex.org/W4285728495","https://openalex.org/W6632774325","https://openalex.org/W6775281218"],"related_works":["https://openalex.org/W1973641256","https://openalex.org/W2047131671","https://openalex.org/W3007838749","https://openalex.org/W2089274067","https://openalex.org/W56994397","https://openalex.org/W1121942432","https://openalex.org/W2181432034","https://openalex.org/W2418069309","https://openalex.org/W4237951173","https://openalex.org/W2376158287"],"abstract_inverted_index":{"Our":[0],"work":[1],"in":[2,16,27,101,120],"this":[3],"paper":[4],"is":[5,89,108],"based":[6],"on":[7,47,112],"the":[8,19,32,37,80,83,122,136,140],"reverse":[9,20,61],"H\u00f6lder-type":[10],"dynamic":[11,22],"inequalities":[12,23,63],"illustrated":[13,24],"by":[14,25],"El-Deeb":[15],"2018":[17],"and":[18,29,44,55,77,94,97],"Hilbert-type":[21,62],"Rezk":[26],"2021":[28],"2022.":[30],"With":[31],"help":[33],"of":[34,39,59,85,132],"Specht\u2019s":[35],"ratio,":[36],"concept":[38],"supermultiplicative":[40,137],"functions,":[41],"chain":[42],"rule,":[43],"Jensen\u2019s":[45],"inequality":[46],"time":[48,67,71,86],"scales,":[49],"we":[50,143],"can":[51],"establish":[52],"some":[53,145],"comprehensive":[54,103],"generalize":[56],"a":[57,65,129],"number":[58],"classical":[60],"to":[64,91,98,125],"general":[66],"scale":[68,72,87],"space.":[69],"In":[70],"calculus,":[73],"results":[74,134,146],"are":[75],"unified":[76],"extended.":[78],"At":[79],"same":[81],"time,":[82],"theory":[84,107],"calculus":[88],"applied":[90,111],"unify":[92],"discrete":[93],"continuous":[95],"analysis":[96],"combine":[99],"them":[100],"one":[102],"form.":[104],"This":[105],"hybrid":[106],"also":[109],"widely":[110],"symmetrical":[113],"properties":[114],"which":[115],"play":[116],"an":[117],"essential":[118],"role":[119],"determining":[121],"correct":[123],"methods":[124],"solve":[126],"inequalities.":[127],"As":[128],"special":[130],"case":[131],"our":[133],"when":[135],"function":[138],"represents":[139],"identity":[141],"map,":[142],"obtain":[144],"that":[147],"have":[148],"been":[149],"recently":[150],"published.":[151]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}