{"id":"https://openalex.org/W3208609347","doi":"https://doi.org/10.3390/axioms10040283","title":"Some New Post-Quantum Integral Inequalities Involving Twice (p, q)-Differentiable \u03c8-Preinvex Functions and Applications","display_name":"Some New Post-Quantum Integral Inequalities Involving Twice (p, q)-Differentiable \u03c8-Preinvex Functions and Applications","publication_year":2021,"publication_date":"2021-10-29","ids":{"openalex":"https://openalex.org/W3208609347","doi":"https://doi.org/10.3390/axioms10040283","mag":"3208609347"},"language":"en","primary_location":{"id":"doi:10.3390/axioms10040283","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10040283","pdf_url":"https://www.mdpi.com/2075-1680/10/4/283/pdf?version=1636076010","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/10/4/283/pdf?version=1636076010","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066464647","display_name":"Miguel Vivas\u2013Cortez","orcid":"https://orcid.org/0000-0002-1567-0264"},"institutions":[{"id":"https://openalex.org/I39398033","display_name":"Pontificia Universidad Cat\u00f3lica del Ecuador","ror":"https://ror.org/02qztda51","country_code":"EC","type":"education","lineage":["https://openalex.org/I39398033"]}],"countries":["EC"],"is_corresponding":false,"raw_author_name":"Miguel Vivas-Cortez","raw_affiliation_strings":["Escuela de Ciencias F\u00edsicas y Matem\u00e1ticas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Cat\u00f3lica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador"],"affiliations":[{"raw_affiliation_string":"Escuela de Ciencias F\u00edsicas y Matem\u00e1ticas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Cat\u00f3lica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador","institution_ids":["https://openalex.org/I39398033"]}]},{"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"],"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/A5052852297","display_name":"Sadia Talib","orcid":"https://orcid.org/0000-0002-9388-9122"},"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":"Sadia Talib","raw_affiliation_strings":["Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"],"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/A5007318507","display_name":"Artion Kashuri","orcid":"https://orcid.org/0000-0003-0115-3079"},"institutions":[{"id":"https://openalex.org/I3130420675","display_name":"University of Vlora \"Ismail Qemali\"","ror":"https://ror.org/05ger6s34","country_code":"AL","type":"education","lineage":["https://openalex.org/I3130420675"]}],"countries":["AL"],"is_corresponding":false,"raw_author_name":"Artion Kashuri","raw_affiliation_strings":["Department of Mathematics, Faculty of Technical Science, University \u201cIsmail Qemali\u201d, 9400 Vlor\u00eb, Albania"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Technical Science, University \u201cIsmail Qemali\u201d, 9400 Vlor\u00eb, Albania","institution_ids":["https://openalex.org/I3130420675"]}]},{"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"],"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":5,"corresponding_author_ids":["https://openalex.org/A5035904409"],"corresponding_institution_ids":["https://openalex.org/I194348271"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.3175,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.79631384,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"10","issue":"4","first_page":"283","last_page":"283"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9725000262260437,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9351999759674072,"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/differentiable-function","display_name":"Differentiable function","score":0.8542622327804565},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7074500918388367},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.7022427916526794},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6020535826683044},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6013765931129456},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.5373676419258118},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.468517541885376},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4478142261505127},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.4437805116176605},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.43430033326148987},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.4211791157722473},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3421180844306946},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3088626563549042},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13639730215072632},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12488088011741638},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09708231687545776}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.8542622327804565},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7074500918388367},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.7022427916526794},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6020535826683044},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6013765931129456},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5373676419258118},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.468517541885376},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4478142261505127},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.4437805116176605},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.43430033326148987},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.4211791157722473},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3421180844306946},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3088626563549042},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13639730215072632},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12488088011741638},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09708231687545776},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms10040283","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10040283","pdf_url":"https://www.mdpi.com/2075-1680/10/4/283/pdf?version=1636076010","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6580d49dcc754a92a345ebb8e41b2f10","is_oa":true,"landing_page_url":"https://doaj.org/article/6580d49dcc754a92a345ebb8e41b2f10","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 10, Iss 4, p 283 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/10/4/283/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms10040283","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":"Axioms; Volume 10; Issue 4; Pages: 283","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms10040283","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10040283","pdf_url":"https://www.mdpi.com/2075-1680/10/4/283/pdf?version=1636076010","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.6700000166893005,"display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320327255","display_name":"Pontificia Universidad Cat\u00f3lica del Ecuador","ror":"https://ror.org/02qztda51"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3208609347.pdf","grobid_xml":"https://content.openalex.org/works/W3208609347.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1963574764","https://openalex.org/W1993803180","https://openalex.org/W2017083850","https://openalex.org/W2018707259","https://openalex.org/W2054550768","https://openalex.org/W2094786643","https://openalex.org/W2109401200","https://openalex.org/W2279269773","https://openalex.org/W2286801957","https://openalex.org/W2516871245","https://openalex.org/W2529427475","https://openalex.org/W2555558966","https://openalex.org/W2567237354","https://openalex.org/W2573131839","https://openalex.org/W2606796707","https://openalex.org/W2614402218","https://openalex.org/W2792363207","https://openalex.org/W2809988703","https://openalex.org/W2893787311","https://openalex.org/W2914763224","https://openalex.org/W2972177571","https://openalex.org/W3015640008","https://openalex.org/W3165796648","https://openalex.org/W3170331393","https://openalex.org/W3174532764","https://openalex.org/W3198326285","https://openalex.org/W3215201654","https://openalex.org/W6648803971","https://openalex.org/W6663971105","https://openalex.org/W6694980441","https://openalex.org/W6696327675","https://openalex.org/W6731064327","https://openalex.org/W6731907626","https://openalex.org/W6776706214"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W1982241170","https://openalex.org/W2116282083","https://openalex.org/W2386549147","https://openalex.org/W1978051046","https://openalex.org/W2012411066","https://openalex.org/W2348722996","https://openalex.org/W4234434982","https://openalex.org/W2904667438"],"abstract_inverted_index":{"The":[0],"main":[1],"motivation":[2],"of":[3,31,38,53],"this":[4],"article":[5],"is":[6],"derive":[7],"a":[8,50],"new":[9,29],"post-quantum":[10],"integral":[11],"identity":[12,20],"using":[13],"twice":[14,58],"(p,":[15,59],"q)-differentiable":[16,60],"functions.":[17,40],"Using":[18],"the":[19,36],"as":[21,68],"an":[22],"auxiliary":[23],"result,":[24],"we":[25,45],"will":[26],"obtain":[27],"some":[28,47],"variants":[30],"Hermite\u2013Hadamard\u2019s":[32],"inequality":[33],"essentially":[34],"via":[35],"class":[37],"\u03c8-preinvex":[39],"To":[41],"support":[42],"our":[43],"results,":[44],"offer":[46],"applications":[48],"to":[49],"special":[51],"means":[52],"positive":[54],"real":[55],"numbers":[56],"and":[57],"functions":[61],"that":[62],"are":[63],"in":[64],"absolute":[65],"value":[66],"bounded":[67],"well.":[69]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2021-11-08T00:00:00"}