{"id":"https://openalex.org/W4317739585","doi":"https://doi.org/10.3390/sym15020301","title":"New Estimation of Error in the Hadamard Inequality Pertaining to Coordinated Convex Functions in Quantum Calculus","display_name":"New Estimation of Error in the Hadamard Inequality Pertaining to Coordinated Convex Functions in Quantum Calculus","publication_year":2023,"publication_date":"2023-01-21","ids":{"openalex":"https://openalex.org/W4317739585","doi":"https://doi.org/10.3390/sym15020301"},"language":"en","primary_location":{"id":"doi:10.3390/sym15020301","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15020301","pdf_url":"https://www.mdpi.com/2073-8994/15/2/301/pdf?version=1674287518","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/2073-8994/15/2/301/pdf?version=1674287518","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054946773","display_name":"Muhammad Raees","orcid":"https://orcid.org/0000-0001-7966-0471"},"institutions":[{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Raees","raw_affiliation_strings":["Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad 44000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-7966-0471","affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I929597975"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101825790","display_name":"Matloob Anwar","orcid":"https://orcid.org/0000-0001-5649-9769"},"institutions":[{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Matloob Anwar","raw_affiliation_strings":["Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad 44000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I929597975"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054946773"],"corresponding_institution_ids":["https://openalex.org/I929597975"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.5021,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50136317,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"15","issue":"2","first_page":"301","last_page":"301"},"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":0.9271000027656555,"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":0.6945558190345764},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6917697191238403},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.6233294010162354},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5878832340240479},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5877150297164917},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5768113136291504},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5559106469154358},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5468572378158569},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.4571303427219391},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.45050010085105896},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44428151845932007},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.43136265873908997},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4245138168334961},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.4129312038421631},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.3481881022453308},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30457672476768494},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.16688159108161926},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11711856722831726}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6945558190345764},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6917697191238403},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.6233294010162354},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5878832340240479},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5877150297164917},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5768113136291504},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5559106469154358},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5468572378158569},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.4571303427219391},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.45050010085105896},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44428151845932007},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.43136265873908997},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4245138168334961},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.4129312038421631},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3481881022453308},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30457672476768494},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16688159108161926},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11711856722831726},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15020301","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15020301","pdf_url":"https://www.mdpi.com/2073-8994/15/2/301/pdf?version=1674287518","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:e6d8e19f603f4154a2784698d337a324","is_oa":false,"landing_page_url":"https://doaj.org/article/e6d8e19f603f4154a2784698d337a324","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 301 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/2/301/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15020301","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; Volume 15; Issue 2; Pages: 301","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15020301","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15020301","pdf_url":"https://www.mdpi.com/2073-8994/15/2/301/pdf?version=1674287518","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":0.6399999856948853,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4317739585.pdf"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W591568057","https://openalex.org/W1963574764","https://openalex.org/W1986128518","https://openalex.org/W1991089207","https://openalex.org/W2009377890","https://openalex.org/W2013621593","https://openalex.org/W2026780626","https://openalex.org/W2035041627","https://openalex.org/W2049558474","https://openalex.org/W2073320441","https://openalex.org/W2082778883","https://openalex.org/W2087120697","https://openalex.org/W2101512155","https://openalex.org/W2108165888","https://openalex.org/W2117619304","https://openalex.org/W2118017323","https://openalex.org/W2166544583","https://openalex.org/W2290236472","https://openalex.org/W2465884706","https://openalex.org/W2499795752","https://openalex.org/W2544427591","https://openalex.org/W2607073263","https://openalex.org/W2952047482","https://openalex.org/W2954571149","https://openalex.org/W2962387070","https://openalex.org/W3030652065","https://openalex.org/W3046153660","https://openalex.org/W3091927652","https://openalex.org/W3108036975","https://openalex.org/W3121690530","https://openalex.org/W3130528407","https://openalex.org/W3136351306","https://openalex.org/W3158612746","https://openalex.org/W3164601652","https://openalex.org/W3164667188","https://openalex.org/W3164956005","https://openalex.org/W3192113741","https://openalex.org/W3194498438","https://openalex.org/W4213175417","https://openalex.org/W4220828459","https://openalex.org/W4234969842","https://openalex.org/W4240644230","https://openalex.org/W6652663081","https://openalex.org/W6676551811","https://openalex.org/W6677706503","https://openalex.org/W6731907626","https://openalex.org/W6736424345","https://openalex.org/W6765624353","https://openalex.org/W6790731554","https://openalex.org/W6791122454"],"related_works":["https://openalex.org/W1996226968","https://openalex.org/W2364547801","https://openalex.org/W4398758929","https://openalex.org/W257189624","https://openalex.org/W2393350255","https://openalex.org/W4390176194","https://openalex.org/W4385382439","https://openalex.org/W4378552409","https://openalex.org/W4293867722","https://openalex.org/W2388570749"],"abstract_inverted_index":{"Convex":[0],"bodies":[1],"are":[2,106],"symmetric":[3],"in":[4,35],"nature.":[5],"Between":[6],"the":[7,22,26,70,99,109,115,118],"two":[8],"variables":[9],"of":[10,30,52,117],"symmetry":[11],"and":[12,73,92,113],"convexity,":[13],"a":[14,45,50,55,74],"correlation":[15],"connection":[16],"is":[17,83],"also":[18],"perceptible.":[19],"Due":[20],"to":[21,98,111],"interchangeable":[23],"analogous":[24],"properties,":[25],"application":[27],"on":[28,44],"either":[29],"them":[31],"has":[32],"been":[33],"practicable":[34],"these":[36],"modern":[37],"years.":[38],"The":[39],"current":[40],"analysis":[41],"sheds":[42],"insight":[43],"general":[46],"new":[47,71,119],"identity":[48,72],"involving":[49],"number":[51],"parameters":[53],"for":[54],"twice":[56,75],"partial":[57,76],"quantum":[58,65,77,101],"differentiable":[59,78],"function.":[60],"We":[61],"find":[62],"several":[63,90],"unique":[64],"integral":[66],"inequalities":[67],"by":[68],"using":[69],"function":[79],"whose":[80],"absolute":[81],"value":[82],"coordinated":[84],"convex.":[85],"In":[86],"addition,":[87],"we":[88],"present":[89],"novel":[91],"interesting":[93],"error":[94],"estimation-like":[95],"results":[96],"related":[97],"well-known":[100],"Hermite\u2013Hadamard":[102],"inequality.":[103],"Some":[104],"examples":[105],"provided":[107],"at":[108],"end":[110],"support":[112],"demonstrate":[114],"effectiveness":[116],"outcomes.":[120]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2023-01-23T00:00:00"}
