{"id":"https://openalex.org/W4394690288","doi":"https://doi.org/10.3390/sym16040457","title":"pq-Simpson\u2019s Type Inequalities Involving Generalized Convexity and Raina\u2019s Function","display_name":"pq-Simpson\u2019s Type Inequalities Involving Generalized Convexity and Raina\u2019s Function","publication_year":2024,"publication_date":"2024-04-09","ids":{"openalex":"https://openalex.org/W4394690288","doi":"https://doi.org/10.3390/sym16040457"},"language":"en","primary_location":{"id":"doi:10.3390/sym16040457","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16040457","pdf_url":"https://www.mdpi.com/2073-8994/16/4/457/pdf?version=1712677172","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/2073-8994/16/4/457/pdf?version=1712677172","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066464647","display_name":"Miguel Jos\u00e9 Vivas Cortez","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, Quito 17-01-2184, Ecuador"],"raw_orcid":"https://orcid.org/0000-0002-1567-0264","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, Quito 17-01-2184, Ecuador","institution_ids":["https://openalex.org/I39398033"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092500866","display_name":"Ghulam Murtaza Baig","orcid":"https://orcid.org/0009-0008-5088-834X"},"institutions":[{"id":"https://openalex.org/I87482320","display_name":"University of Management and Technology","ror":"https://ror.org/0095xcq10","country_code":"PK","type":"education","lineage":["https://openalex.org/I87482320"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Ghulam Murtaza Baig","raw_affiliation_strings":["Department of Mathematics, University of Management and Technology C-II, Lahore 54700, Pakistan"],"raw_orcid":"https://orcid.org/0009-0008-5088-834X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Management and Technology C-II, Lahore 54700, Pakistan","institution_ids":["https://openalex.org/I87482320"]}]},{"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":"last","author":{"id":"https://openalex.org/A5090557210","display_name":"Kamel Brahim","orcid":"https://orcid.org/0000-0002-7113-8651"},"institutions":[{"id":"https://openalex.org/I4210136004","display_name":"University of Bisha","ror":"https://ror.org/040548g92","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210136004"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Kamel Brahim","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Bisha, P.O. Box 551, Bisha 61922, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Bisha, P.O. Box 551, Bisha 61922, Saudi Arabia","institution_ids":["https://openalex.org/I4210136004"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"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":0.8763,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.65462809,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"16","issue":"4","first_page":"457","last_page":"457"},"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":0.9445000290870667,"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/convexity","display_name":"Convexity","score":0.8358631134033203},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.689507782459259},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6819837093353271},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6335187554359436},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.6192792654037476},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5576611161231995},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.5549331307411194},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5226866006851196},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.49583539366722107},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.47446995973587036},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39158451557159424},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38911503553390503},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14299708604812622},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10398295521736145},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08943790197372437}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8358631134033203},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.689507782459259},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6819837093353271},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6335187554359436},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.6192792654037476},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5576611161231995},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5549331307411194},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5226866006851196},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.49583539366722107},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.47446995973587036},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39158451557159424},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38911503553390503},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14299708604812622},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10398295521736145},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08943790197372437},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16040457","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16040457","pdf_url":"https://www.mdpi.com/2073-8994/16/4/457/pdf?version=1712677172","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:d881d9df95724b5194684ac7a259f344","is_oa":false,"landing_page_url":"https://doaj.org/article/d881d9df95724b5194684ac7a259f344","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 16, Iss 4, p 457 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16040457","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16040457","pdf_url":"https://www.mdpi.com/2073-8994/16/4/457/pdf?version=1712677172","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":0.5899999737739563,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G4754070141","display_name":null,"funder_award_id":"070-UIO-2022","funder_id":"https://openalex.org/F4320327255","funder_display_name":"Pontificia Universidad Cat\u00f3lica del Ecuador"}],"funders":[{"id":"https://openalex.org/F4320319621","display_name":"University of Bisha","ror":"https://ror.org/040548g92"},{"id":"https://openalex.org/F4320327255","display_name":"Pontificia Universidad Cat\u00f3lica del Ecuador","ror":"https://ror.org/02qztda51"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4394690288.pdf","grobid_xml":"https://content.openalex.org/works/W4394690288.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W59400897","https://openalex.org/W61423009","https://openalex.org/W155259267","https://openalex.org/W254209083","https://openalex.org/W566543047","https://openalex.org/W2054550768","https://openalex.org/W2066273251","https://openalex.org/W2084967964","https://openalex.org/W2118017323","https://openalex.org/W2183169701","https://openalex.org/W2529427475","https://openalex.org/W2614402218","https://openalex.org/W2790013524","https://openalex.org/W2903641028","https://openalex.org/W2977556055","https://openalex.org/W2985192472","https://openalex.org/W3006443523","https://openalex.org/W3016416088","https://openalex.org/W3019425015","https://openalex.org/W3030308006","https://openalex.org/W3030652065","https://openalex.org/W3045278394","https://openalex.org/W3046153660","https://openalex.org/W3101401782","https://openalex.org/W3108036975","https://openalex.org/W3124251384","https://openalex.org/W3164806255","https://openalex.org/W3164956005","https://openalex.org/W3167636301","https://openalex.org/W3170865853","https://openalex.org/W3174676267","https://openalex.org/W3215201654","https://openalex.org/W4205977837","https://openalex.org/W4240644230","https://openalex.org/W4291016807","https://openalex.org/W4384823329","https://openalex.org/W4385272874","https://openalex.org/W4385805742","https://openalex.org/W6606375086","https://openalex.org/W6609593801","https://openalex.org/W6663971105","https://openalex.org/W6671893725","https://openalex.org/W6686337283"],"related_works":["https://openalex.org/W2366107444","https://openalex.org/W2912909874","https://openalex.org/W4288573727","https://openalex.org/W2494876756","https://openalex.org/W2768754015","https://openalex.org/W4398758929","https://openalex.org/W257189624","https://openalex.org/W2393350255","https://openalex.org/W4390176194","https://openalex.org/W4387635768"],"abstract_inverted_index":{"This":[0],"study":[1],"uses":[2],"Raina\u2019s":[3],"function":[4],"to":[5],"obtain":[6],"a":[7],"new":[8,18],"coordinated":[9,40],"pq-integral":[10],"identity.":[11],"Using":[12],"this":[13],"identity,":[14],"we":[15],"construct":[16],"several":[17],"pq-Simpson\u2019s":[19],"type":[20,37],"inequalities":[21,32,38],"for":[22,39,49],"generalized":[23,41],"convex":[24,42],"functions":[25],"on":[26],"coordinates.":[27],"Setting":[28],"p1=p2=1":[29],"in":[30],"these":[31],"yields":[33],"well-known":[34],"quantum":[35,54],"Simpson\u2019s":[36],"functions.":[43],"Our":[44],"results":[45],"have":[46],"important":[47],"implications":[48],"the":[50],"creation":[51],"of":[52],"post":[53],"mathematical":[55],"frameworks.":[56]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-09T15:46:55.921056","created_date":"2025-10-10T00:00:00"}