{"id":"https://openalex.org/W4306773596","doi":"https://doi.org/10.3390/sym14102187","title":"Jensen-Mercer Type Inequalities in the Setting of Fractional Calculus with Applications","display_name":"Jensen-Mercer Type Inequalities in the Setting of Fractional Calculus with Applications","publication_year":2022,"publication_date":"2022-10-18","ids":{"openalex":"https://openalex.org/W4306773596","doi":"https://doi.org/10.3390/sym14102187"},"language":"en","primary_location":{"id":"doi:10.3390/sym14102187","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14102187","pdf_url":"https://www.mdpi.com/2073-8994/14/10/2187/pdf?version=1666084968","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/2073-8994/14/10/2187/pdf?version=1666084968","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/A5024231129","display_name":"Marcela V. Mihai","orcid":"https://orcid.org/0000-0002-4864-8899"},"institutions":[{"id":"https://openalex.org/I4210088507","display_name":"Romanian Society of Nephrology","ror":"https://ror.org/003tbyf39","country_code":"RO","type":"other","lineage":["https://openalex.org/I4210088507"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Marcela V. Mihai","raw_affiliation_strings":["Department Scientific-Methodical Sessions, Romanian Mathematical Society-Branch Bucharest, Academy Street no. 14, RO-010014 Bucharest, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department Scientific-Methodical Sessions, Romanian Mathematical Society-Branch Bucharest, Academy Street no. 14, RO-010014 Bucharest, Romania","institution_ids":["https://openalex.org/I4210088507"]}]},{"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/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 38000, Pakistan"],"raw_orcid":null,"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/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 4000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-6105-2435","affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Islamabad 4000, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"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":1.7778,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.84208169,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"14","issue":"10","first_page":"2187","last_page":"2187"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.9835000038146973,"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":0.8036145567893982},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.7490391731262207},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6025047302246094},{"id":"https://openalex.org/keywords/jensens-inequality","display_name":"Jensen's inequality","score":0.5616879463195801},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5420542359352112},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.45604613423347473},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.4507746696472168},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42292332649230957},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4128188490867615},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3929522633552551},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3632861375808716},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21704146265983582},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.19940891861915588},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.13696837425231934},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.05319008231163025}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8036145567893982},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.7490391731262207},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6025047302246094},{"id":"https://openalex.org/C174169938","wikidata":"https://www.wikidata.org/wiki/Q518131","display_name":"Jensen's inequality","level":5,"score":0.5616879463195801},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5420542359352112},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.45604613423347473},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.4507746696472168},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42292332649230957},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4128188490867615},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3929522633552551},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3632861375808716},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21704146265983582},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.19940891861915588},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.13696837425231934},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.05319008231163025},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/sym14102187","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14102187","pdf_url":"https://www.mdpi.com/2073-8994/14/10/2187/pdf?version=1666084968","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:20.500.12684/12446","is_oa":true,"landing_page_url":"https://hdl.handle.net/20.500.12684/12446","pdf_url":"https://acikerisim.duzce.edu.tr/bitstreams/2187b809-6e30-4fe2-9133-2579fc52374a/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:c7fd341b-0ac5-42c6-b004-23e6ab603092","is_oa":false,"landing_page_url":"https://avesis.kocaeli.edu.tr/publication/details/c7fd341b-0ac5-42c6-b004-23e6ab603092/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:a4ada81086af4a48b9223e73eff4c5f4","is_oa":true,"landing_page_url":"https://doaj.org/article/a4ada81086af4a48b9223e73eff4c5f4","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 10, p 2187 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/10/2187/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14102187","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/sym14102187","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14102187","pdf_url":"https://www.mdpi.com/2073-8994/14/10/2187/pdf?version=1666084968","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/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"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4306773596.pdf"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W47555992","https://openalex.org/W254209083","https://openalex.org/W2006458314","https://openalex.org/W2048753115","https://openalex.org/W2055229129","https://openalex.org/W2072882480","https://openalex.org/W2318666342","https://openalex.org/W2323279258","https://openalex.org/W2469986892","https://openalex.org/W2514595787","https://openalex.org/W2556784265","https://openalex.org/W2570306563","https://openalex.org/W2603194489","https://openalex.org/W2789458122","https://openalex.org/W2799512039","https://openalex.org/W2884999737","https://openalex.org/W2901654626","https://openalex.org/W2903641028","https://openalex.org/W2944829413","https://openalex.org/W2951351560","https://openalex.org/W2963641381","https://openalex.org/W2970328856","https://openalex.org/W3008956162","https://openalex.org/W3013345958","https://openalex.org/W3022413018","https://openalex.org/W3035692153","https://openalex.org/W3048865070","https://openalex.org/W3082976077","https://openalex.org/W3098144555","https://openalex.org/W3098627266","https://openalex.org/W3105863746","https://openalex.org/W3211008961","https://openalex.org/W3214938231","https://openalex.org/W4205249021","https://openalex.org/W4210808694","https://openalex.org/W4220755736","https://openalex.org/W6609593801","https://openalex.org/W6668615881","https://openalex.org/W6730176618","https://openalex.org/W6735588220","https://openalex.org/W6751254201","https://openalex.org/W6756652536","https://openalex.org/W6775924873","https://openalex.org/W6782652466","https://openalex.org/W6785963344","https://openalex.org/W6803277159"],"related_works":["https://openalex.org/W2111217632","https://openalex.org/W4293557899","https://openalex.org/W4396753818","https://openalex.org/W4294618985","https://openalex.org/W2518252082","https://openalex.org/W2364547801","https://openalex.org/W4206144597","https://openalex.org/W4200119807","https://openalex.org/W2788930696","https://openalex.org/W4301016436"],"abstract_inverted_index":{"The":[0],"main":[1,42,57],"objective":[2],"of":[3,12,28,40,55],"this":[4],"paper":[5],"is":[6],"to":[7,37,64,68],"establish":[8],"some":[9,24,39,61],"new":[10,25,47],"variants":[11],"the":[13,53],"Jensen\u2013Mercer":[14],"inequality":[15],"via":[16],"harmonically":[17],"strongly":[18],"convex":[19],"function.":[20],"We":[21],"also":[22,45],"propose":[23],"fractional":[26,33,48],"analogues":[27],"Hermite\u2013Hadamard\u2013Jensen\u2013Mercer-like":[29],"inequalities":[30],"using":[31],"AB":[32],"integrals.":[34],"In":[35],"order":[36],"obtain":[38],"our":[41,56],"results,":[43,58],"we":[44,59],"derive":[46],"integral":[49],"identities.":[50],"To":[51],"demonstrate":[52],"significance":[54],"present":[60],"interesting":[62],"applications":[63],"special":[65],"means":[66],"and":[67],"error":[69],"bounds":[70],"as":[71],"well.":[72]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}