{"id":"https://openalex.org/W4376875020","doi":"https://doi.org/10.3390/sym15051096","title":"Exploration of Quantum Milne\u2013Mercer-Type Inequalities with Applications","display_name":"Exploration of Quantum Milne\u2013Mercer-Type Inequalities with Applications","publication_year":2023,"publication_date":"2023-05-16","ids":{"openalex":"https://openalex.org/W4376875020","doi":"https://doi.org/10.3390/sym15051096"},"language":"en","primary_location":{"id":"doi:10.3390/sym15051096","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051096","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1096/pdf?version=1684375215","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/2073-8994/15/5/1096/pdf?version=1684375215","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078588265","display_name":"Bandar Bin\u2010Mohsin","orcid":"https://orcid.org/0000-0002-2160-4159"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Bandar Bin-Mohsin","raw_affiliation_strings":["Department of Mathematics, College of Science, King Saud University, Riyadh 145111, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Saud University, Riyadh 145111, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069757223","display_name":"Muhammad Zakria Javed","orcid":"https://orcid.org/0000-0001-5212-6252"},"institutions":[{"id":"https://openalex.org/I194348271","display_name":"Government College University, Faisalabad","ror":"https://ror.org/051zgra59","country_code":"PK","type":"education","lineage":["https://openalex.org/I194348271"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Zakria Javed","raw_affiliation_strings":["Department of Mathematics, Government College University, Faisalabad 54000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-5212-6252","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad 54000, Pakistan","institution_ids":["https://openalex.org/I194348271"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035904409","display_name":"Muhammad Uzair Awan","orcid":"https://orcid.org/0000-0002-1019-9485"},"institutions":[{"id":"https://openalex.org/I194348271","display_name":"Government College University, Faisalabad","ror":"https://ror.org/051zgra59","country_code":"PK","type":"education","lineage":["https://openalex.org/I194348271"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Uzair Awan","raw_affiliation_strings":["Department of Mathematics, Government College University, Faisalabad 54000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-1019-9485","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad 54000, Pakistan","institution_ids":["https://openalex.org/I194348271"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072105958","display_name":"Awais Gul Khan","orcid":"https://orcid.org/0000-0003-4914-5959"},"institutions":[{"id":"https://openalex.org/I194348271","display_name":"Government College University, Faisalabad","ror":"https://ror.org/051zgra59","country_code":"PK","type":"education","lineage":["https://openalex.org/I194348271"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Awais Gul Khan","raw_affiliation_strings":["Department of Mathematics, Government College University, Faisalabad 54000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad 54000, Pakistan","institution_ids":["https://openalex.org/I194348271"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080017749","display_name":"Clemente Cesarano","orcid":"https://orcid.org/0000-0002-1694-7907"},"institutions":[{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Clemente Cesarano","raw_affiliation_strings":["Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy","institution_ids":["https://openalex.org/I4210155399"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087578803","display_name":"Muhammad Aslam Noor","orcid":"https://orcid.org/0000-0001-6105-2435"},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Aslam Noor","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-6105-2435","affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5035904409"],"corresponding_institution_ids":["https://openalex.org/I194348271"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":10.0456,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.99043744,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"15","issue":"5","first_page":"1096","last_page":"1096"},"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":0.9824000000953674,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9527000188827515,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/type","display_name":"Type (biology)","score":0.6345149874687195},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6292605400085449},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6239632964134216},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6094354391098022},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.5192882418632507},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5017962455749512},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4820059835910797},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4550108313560486},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.4493945240974426},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4133497476577759},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4065145254135132},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4020807147026062},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11462736129760742}],"concepts":[{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6345149874687195},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6292605400085449},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6239632964134216},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6094354391098022},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5192882418632507},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5017962455749512},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4820059835910797},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4550108313560486},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.4493945240974426},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4133497476577759},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4065145254135132},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4020807147026062},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11462736129760742},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15051096","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051096","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1096/pdf?version=1684375215","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:6ce3eca53b1a4c82afeb1b7200014367","is_oa":false,"landing_page_url":"https://doaj.org/article/6ce3eca53b1a4c82afeb1b7200014367","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 5, p 1096 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/5/1096/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15051096","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/sym15051096","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051096","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1096/pdf?version=1684375215","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":0.5799999833106995,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G3908898470","display_name":null,"funder_award_id":"RSP2023R158","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"}],"funders":[{"id":"https://openalex.org/F4320321145","display_name":"King Saud University","ror":"https://ror.org/02f81g417"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4376875020.pdf"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W2011117896","https://openalex.org/W2054550768","https://openalex.org/W2077442372","https://openalex.org/W2089284592","https://openalex.org/W2118017323","https://openalex.org/W2128181058","https://openalex.org/W2516871245","https://openalex.org/W2529427475","https://openalex.org/W2603194489","https://openalex.org/W2962387070","https://openalex.org/W3006443523","https://openalex.org/W3010570299","https://openalex.org/W3015825894","https://openalex.org/W3030652065","https://openalex.org/W3033036396","https://openalex.org/W3035692153","https://openalex.org/W3046153660","https://openalex.org/W3096678151","https://openalex.org/W3164956005","https://openalex.org/W3173191086","https://openalex.org/W4205249021","https://openalex.org/W4205856715","https://openalex.org/W4226495852","https://openalex.org/W4240644230","https://openalex.org/W4293527416","https://openalex.org/W4313398728","https://openalex.org/W4313414257","https://openalex.org/W4317212691","https://openalex.org/W4317739585","https://openalex.org/W4317791703","https://openalex.org/W4319599449","https://openalex.org/W4361298751","https://openalex.org/W6663971105","https://openalex.org/W6735588220","https://openalex.org/W6778680190","https://openalex.org/W6779056946"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W2334570605","https://openalex.org/W3181683615","https://openalex.org/W4286826125","https://openalex.org/W1633485514","https://openalex.org/W2914542058","https://openalex.org/W4385382439","https://openalex.org/W4387635768"],"abstract_inverted_index":{"Quantum":[0],"calculus":[1,15],"provides":[2],"a":[3,31,73,91],"significant":[4],"generalization":[5],"of":[6,13,27,35,42,55,77,114,133,139],"classical":[7,14,28],"concepts":[8],"and":[9,84,106,126,153,159],"overcomes":[10],"the":[11,21,53,56,78,102,115,131,137,144],"limitations":[12],"in":[16,37],"tackling":[17],"non-differentiable":[18],"functions.":[19],"Implementing":[20],"q-concepts":[22],"to":[23,46,65,82,109,129,147,163],"obtain":[24,110],"fresh":[25],"variants":[26],"outcomes":[29],"is":[30,45,143],"very":[32],"intriguing":[33],"aspect":[34],"research":[36],"mathematical":[38],"analysis.":[39],"The":[40],"objective":[41],"this":[43,67,142,168],"article":[44,146],"establish":[47],"novel":[48],"Milne-type":[49],"integral":[50],"inequalities":[51,152],"through":[52],"utilization":[54],"Mercer":[57],"inequality":[58],"for":[59,94],"q-differentiable":[60],"convex":[61,107],"mappings.":[62],"In":[63],"order":[64],"accomplish":[66],"task,":[68],"we":[69,154],"begin":[70],"by":[71],"demonstrating":[72],"new":[74,111],"quantum":[75,150],"identity":[76],"Milne":[79],"type":[80],"linked":[81],"left":[83],"right":[85],"q":[86],"derivatives.":[87],"This":[88],"serves":[89],"as":[90],"supporting":[92],"result":[93],"our":[95,134,140,157],"primary":[96],"findings.":[97],"Our":[98],"approach":[99],"involves":[100],"using":[101],"q-equality,":[103],"well-known":[104],"inequalities,":[105],"mappings":[108],"error":[112],"bounds":[113],"Milne\u2013Mercer":[116],"type.":[117],"We":[118],"also":[119],"provide":[120],"some":[121],"special":[122],"cases,":[123],"numerical":[124],"examples,":[125],"graphical":[127],"analysis":[128],"evaluate":[130],"efficacy":[132],"results.":[135],"To":[136],"best":[138],"knowledge,":[141],"first":[145],"focus":[148],"on":[149],"Milne\u2013Mercer-type":[151],"hope":[155],"that":[156],"methods":[158],"findings":[160],"inspire":[161],"readers":[162],"conduct":[164],"further":[165],"investigation":[166],"into":[167],"problem.":[169]},"counts_by_year":[{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2023-05-18T00:00:00"}