{"id":"https://openalex.org/W4295942273","doi":"https://doi.org/10.3390/sym14091925","title":"Quantum Integral Inequalities in the Setting of Majorization Theory and Applications","display_name":"Quantum Integral Inequalities in the Setting of Majorization Theory and Applications","publication_year":2022,"publication_date":"2022-09-14","ids":{"openalex":"https://openalex.org/W4295942273","doi":"https://doi.org/10.3390/sym14091925"},"language":"en","primary_location":{"id":"doi:10.3390/sym14091925","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091925","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1925/pdf?version=1663805685","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/2073-8994/14/9/1925/pdf?version=1663805685","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 11451, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Saud University, Riyadh 11451, 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 38000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-5212-6252","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad 38000, 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 38000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-1019-9485","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan","institution_ids":["https://openalex.org/I194348271"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071456926","display_name":"H\u00fcseyin Budak","orcid":"https://orcid.org/0000-0001-8843-955X"},"institutions":[{"id":"https://openalex.org/I54001450","display_name":"D\u00fczce \u00dcniversitesi","ror":"https://ror.org/04175wc52","country_code":"TR","type":"education","lineage":["https://openalex.org/I54001450"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"H\u00fcseyin Budak","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Arts, D\u00fczce University, D\u00fczce 81620, Turkey"],"raw_orcid":"https://orcid.org/0000-0001-8843-955X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Arts, D\u00fczce University, D\u00fczce 81620, Turkey","institution_ids":["https://openalex.org/I54001450"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036300550","display_name":"Hasan Kara","orcid":"https://orcid.org/0000-0002-2075-944X"},"institutions":[{"id":"https://openalex.org/I54001450","display_name":"D\u00fczce \u00dcniversitesi","ror":"https://ror.org/04175wc52","country_code":"TR","type":"education","lineage":["https://openalex.org/I54001450"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Hasan Kara","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Arts, D\u00fczce University, D\u00fczce 81620, Turkey"],"raw_orcid":"https://orcid.org/0000-0002-2075-944X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Arts, D\u00fczce University, D\u00fczce 81620, Turkey","institution_ids":["https://openalex.org/I54001450"]}]},{"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 44000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-6105-2435","affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, 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":2.4889,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.89355377,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"14","issue":"9","first_page":"1925","last_page":"1925"},"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/T12508","display_name":"Functional Equations Stability Results","score":0.9562000036239624,"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":0.9442999958992004,"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":0.7949583530426025},{"id":"https://openalex.org/keywords/majorization","display_name":"Majorization","score":0.7858318090438843},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.607603132724762},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5590624809265137},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5011734962463379},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.49880075454711914},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.47184112668037415},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.4689680337905884},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.46867164969444275},{"id":"https://openalex.org/keywords/jensens-inequality","display_name":"Jensen's inequality","score":0.45186832547187805},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.4310036301612854},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.4121336340904236},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4101380407810211},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36499637365341187},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3556020259857178},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.27589690685272217},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.2575790286064148},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18447595834732056}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7949583530426025},{"id":"https://openalex.org/C2777818330","wikidata":"https://www.wikidata.org/wiki/Q1994695","display_name":"Majorization","level":2,"score":0.7858318090438843},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.607603132724762},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5590624809265137},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5011734962463379},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.49880075454711914},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.47184112668037415},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.4689680337905884},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.46867164969444275},{"id":"https://openalex.org/C174169938","wikidata":"https://www.wikidata.org/wiki/Q518131","display_name":"Jensen's inequality","level":5,"score":0.45186832547187805},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.4310036301612854},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.4121336340904236},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4101380407810211},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36499637365341187},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3556020259857178},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.27589690685272217},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2575790286064148},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18447595834732056},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/sym14091925","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091925","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1925/pdf?version=1663805685","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:acikerisim.duzce.edu.tr:20.500.12684/12548","is_oa":true,"landing_page_url":"https://hdl.handle.net/20.500.12684/12548","pdf_url":"https://acikerisim.duzce.edu.tr/bitstreams/c34d95e6-fc57-4d81-980d-e40ee9891f04/download","source":{"id":"https://openalex.org/S4377196355","display_name":"DSpace - D\u00fczce (Duzce University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54001450","host_organization_name":"D\u00fczce \u00dcniversitesi","host_organization_lineage":["https://openalex.org/I54001450"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:c579d166-9a48-4525-94e0-2eac7cb0e3a5","is_oa":false,"landing_page_url":"https://avesis.kocaeli.edu.tr/publication/details/c579d166-9a48-4525-94e0-2eac7cb0e3a5/oai","pdf_url":null,"source":{"id":"https://openalex.org/S7407055291","display_name":"Kocaeli \u00dcniversitesi - AVES\u0130S","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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:4d1e8b67fde84d12a74aed183ee49094","is_oa":true,"landing_page_url":"https://doaj.org/article/4d1e8b67fde84d12a74aed183ee49094","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 9, p 1925 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/9/1925/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14091925","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/sym14091925","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091925","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1925/pdf?version=1663805685","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":0.47999998927116394,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G3907851594","display_name":null,"funder_award_id":"RSP-2021/158","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"},{"id":"https://openalex.org/G7545718068","display_name":null,"funder_award_id":"RSP-2021","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"},{"id":"https://openalex.org/F4320326275","display_name":"Higher Education Commision, Pakistan","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4295942273.pdf"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1987113198","https://openalex.org/W2036214360","https://openalex.org/W2054550768","https://openalex.org/W2066273251","https://openalex.org/W2118017323","https://openalex.org/W2128181058","https://openalex.org/W2516871245","https://openalex.org/W2529427475","https://openalex.org/W2603194489","https://openalex.org/W2893787311","https://openalex.org/W2903641028","https://openalex.org/W3006443523","https://openalex.org/W3033036396","https://openalex.org/W3035692153","https://openalex.org/W3040789250","https://openalex.org/W3040855343","https://openalex.org/W3088957435","https://openalex.org/W3105863746","https://openalex.org/W4200389032","https://openalex.org/W4205249021","https://openalex.org/W4210371360","https://openalex.org/W4210808694","https://openalex.org/W4213278223","https://openalex.org/W4226495852","https://openalex.org/W4280525423","https://openalex.org/W4283328530","https://openalex.org/W6659212356","https://openalex.org/W6663971105","https://openalex.org/W6735588220","https://openalex.org/W6779056946"],"related_works":["https://openalex.org/W4396753818","https://openalex.org/W3194917076","https://openalex.org/W4294618985","https://openalex.org/W2518252082","https://openalex.org/W2107607730","https://openalex.org/W2364547801","https://openalex.org/W4206144597","https://openalex.org/W4286749488","https://openalex.org/W2946322567","https://openalex.org/W2991397262"],"abstract_inverted_index":{"In":[0,30,69],"recent":[1],"years,":[2],"the":[3,67,78,82,97,137,153,160,168,192],"theory":[4,60],"of":[5,21,44,84,99,140,155,162,170,182,194],"convex":[6,45],"mappings":[7,46],"has":[8,24],"gained":[9],"much":[10],"more":[11],"attention":[12],"due":[13],"to":[14,148],"its":[15,103],"massive":[16],"utility":[17],"in":[18,66,81],"different":[19,28],"fields":[20],"mathematics.":[22],"It":[23],"been":[25,64],"characterized":[26],"by":[27],"approaches.":[29],"1929,":[31],"G.":[32,39],"H.":[33],"Hardy,":[34],"J.":[35],"E.":[36],"Littlewood,":[37],"and":[38,86,102,136],"Polya":[40],"established":[41],"another":[42],"characterization":[43],"involving":[47],"an":[48],"ordering":[49],"relationship":[50],"defined":[51],"over":[52],"Rn":[53],"known":[54],"as":[55],"majorization":[56],"theory.":[57],"Using":[58],"this":[59,70,129,195],"many":[61],"inequalities":[62,76,95,135],"have":[63],"obtained":[65],"literature.":[68],"paper,":[71],"we":[72,90,113,123,131,165,177],"study":[73],"Hermite\u2013Hadamard":[74],"type":[75,94],"using":[77],"Jensen\u2013Mercer":[79],"inequality":[80,101],"frame":[83],"q\u02d9-calculus":[85],"majorized":[87],"l-tuples.":[88],"Firstly":[89],"derive":[91],"q\u02d9-Hermite\u2013Hadamard\u2013Jensen\u2013Mercer":[92],"(H.H.J.M)":[93],"with":[96,175],"help":[98,161],"Mercer\u2019s":[100],"weighted":[104],"form.":[105],"To":[106],"obtain":[107,124],"some":[108,125,146,179],"new":[109],"generalized":[110,116],"(H.H.J.M)-type":[111],"inequalities,":[112],"prove":[114],"a":[115],"quantum":[117],"identity":[118],"for":[119,128],"q\u02d9-differentiable":[120],"mappings.":[121,141],"Next,":[122],"estimation-type":[126],"results;":[127],"purpose,":[130],"consider":[132],"q\u02d9-identity,":[133],"fundamental":[134],"convexity":[138],"property":[139],"Later":[142],"on,":[143],"We":[144],"offer":[145],"applications":[147],"special":[149],"means":[150],"that":[151,187],"demonstrate":[152],"importance":[154],"our":[156,171,183],"main":[157,172,184],"results.":[158],"With":[159],"numerical":[163],"examples,":[164],"also":[166],"check":[167],"validity":[169],"outcomes.":[173],"Along":[174],"this,":[176],"present":[178],"graphical":[180],"analyses":[181],"results":[185,193],"so":[186],"readers":[188],"may":[189],"easily":[190],"grasp":[191],"paper.":[196]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}