{"id":"https://openalex.org/W4313407410","doi":"https://doi.org/10.3390/sym14122682","title":"A Study on the Modified Form of Riemann-Type Fractional Inequalities via Convex Functions and Related Applications","display_name":"A Study on the Modified Form of Riemann-Type Fractional Inequalities via Convex Functions and Related Applications","publication_year":2022,"publication_date":"2022-12-19","ids":{"openalex":"https://openalex.org/W4313407410","doi":"https://doi.org/10.3390/sym14122682"},"language":"en","primary_location":{"id":"doi:10.3390/sym14122682","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14122682","pdf_url":"https://www.mdpi.com/2073-8994/14/12/2682/pdf?version=1671429298","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/2073-8994/14/12/2682/pdf?version=1671429298","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065292084","display_name":"Muhammad Samraiz","orcid":"https://orcid.org/0000-0001-8480-2817"},"institutions":[{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Samraiz","raw_affiliation_strings":["Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-8480-2817","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038389210","display_name":"Maria Malik","orcid":null},"institutions":[{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Maria Malik","raw_affiliation_strings":["Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053462407","display_name":"Kanwal Saeed","orcid":null},"institutions":[{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Kanwal Saeed","raw_affiliation_strings":["Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088077093","display_name":"Saima Naheed","orcid":"https://orcid.org/0000-0003-1984-525X"},"institutions":[{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Saima Naheed","raw_affiliation_strings":["Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078232638","display_name":"Sina Etemad","orcid":"https://orcid.org/0000-0002-1574-1800"},"institutions":[{"id":"https://openalex.org/I51301133","display_name":"Azarbaijan Shahid Madani University","ror":"https://ror.org/05pg2cw06","country_code":"IR","type":"education","lineage":["https://openalex.org/I51301133"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Sina Etemad","raw_affiliation_strings":["Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran"],"raw_orcid":"https://orcid.org/0000-0002-1574-1800","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran","institution_ids":["https://openalex.org/I51301133"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042326806","display_name":"Manuel De la Sen","orcid":"https://orcid.org/0000-0001-9320-9433"},"institutions":[{"id":"https://openalex.org/I169108374","display_name":"University of the Basque Country","ror":"https://ror.org/000xsnr85","country_code":"ES","type":"education","lineage":["https://openalex.org/I169108374"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Manuel De la Sen","raw_affiliation_strings":["Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country (UPV/EHU), 48940 Leioa, Bizkaia, Spain"],"raw_orcid":"https://orcid.org/0000-0001-9320-9433","affiliations":[{"raw_affiliation_string":"Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country (UPV/EHU), 48940 Leioa, Bizkaia, Spain","institution_ids":["https://openalex.org/I169108374"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053506086","display_name":"Shahram Rezapour","orcid":"https://orcid.org/0000-0003-3463-2607"},"institutions":[{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]},{"id":"https://openalex.org/I4210126829","display_name":"China Medical University Hospital","ror":"https://ror.org/0368s4g32","country_code":"TW","type":"healthcare","lineage":["https://openalex.org/I4210126829"]},{"id":"https://openalex.org/I51301133","display_name":"Azarbaijan Shahid Madani University","ror":"https://ror.org/05pg2cw06","country_code":"IR","type":"education","lineage":["https://openalex.org/I51301133"]}],"countries":["IR","TW"],"is_corresponding":true,"raw_author_name":"Shahram Rezapour","raw_affiliation_strings":["Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran","Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"],"raw_orcid":"https://orcid.org/0000-0003-3463-2607","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran","institution_ids":["https://openalex.org/I51301133"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan","institution_ids":["https://openalex.org/I4210126829","https://openalex.org/I184693016"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5042326806","https://openalex.org/A5053506086","https://openalex.org/A5078232638"],"corresponding_institution_ids":["https://openalex.org/I169108374","https://openalex.org/I184693016","https://openalex.org/I4210126829","https://openalex.org/I51301133"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.0667,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.76039418,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"14","issue":"12","first_page":"2682","last_page":"2682"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":1.0,"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":1.0,"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":0.9362999796867371,"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":0.7149297595024109},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6160796880722046},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5419825315475464},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5038461089134216},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5035211443901062},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.4685424566268921},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.46782535314559937},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4468218684196472},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41750991344451904},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38694465160369873}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7149297595024109},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6160796880722046},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5419825315475464},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5038461089134216},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5035211443901062},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.4685424566268921},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.46782535314559937},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4468218684196472},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41750991344451904},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38694465160369873},{"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":4,"locations":[{"id":"doi:10.3390/sym14122682","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14122682","pdf_url":"https://www.mdpi.com/2073-8994/14/12/2682/pdf?version=1671429298","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:addi.ehu.eus:10810/59242","is_oa":true,"landing_page_url":"http://hdl.handle.net/10810/59242","pdf_url":null,"source":{"id":"https://openalex.org/S4306401964","display_name":"Communities in ADDI (University of the Basque Country)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169108374","host_organization_name":"University of the Basque Country","host_organization_lineage":["https://openalex.org/I169108374"],"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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:30603bb612604f118d469be88a42aef1","is_oa":true,"landing_page_url":"https://doaj.org/article/30603bb612604f118d469be88a42aef1","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 12, p 2682 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/12/2682/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14122682","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/sym14122682","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14122682","pdf_url":"https://www.mdpi.com/2073-8994/14/12/2682/pdf?version=1671429298","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":[{"display_name":"Reduced inequalities","score":0.4399999976158142,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4313407410.pdf"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W433794350","https://openalex.org/W2048305092","https://openalex.org/W2056135743","https://openalex.org/W2103233901","https://openalex.org/W2318890204","https://openalex.org/W2560939205","https://openalex.org/W2768852698","https://openalex.org/W2800098685","https://openalex.org/W2898923932","https://openalex.org/W2900451839","https://openalex.org/W2949897179","https://openalex.org/W2980842028","https://openalex.org/W3000320805","https://openalex.org/W3015825894","https://openalex.org/W3032645491","https://openalex.org/W3033589593","https://openalex.org/W3047289956","https://openalex.org/W3047793579","https://openalex.org/W3085558482","https://openalex.org/W3125115167","https://openalex.org/W3126850697","https://openalex.org/W3129164548","https://openalex.org/W3142469695","https://openalex.org/W3154306151","https://openalex.org/W3198469288","https://openalex.org/W4207037442","https://openalex.org/W4210274926","https://openalex.org/W4220913035","https://openalex.org/W4221052207","https://openalex.org/W4224247972","https://openalex.org/W4226092131","https://openalex.org/W4281717566","https://openalex.org/W4293084153","https://openalex.org/W4294352899","https://openalex.org/W4311505376","https://openalex.org/W6731054983","https://openalex.org/W6763536426","https://openalex.org/W6807131331","https://openalex.org/W6838594276","https://openalex.org/W6842285697"],"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/W2788930696","https://openalex.org/W4301016436","https://openalex.org/W4293867722","https://openalex.org/W4297791001"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3],"provide":[4],"constraints":[5],"for":[6,27,39,56,66],"the":[7,57,67,71],"sum":[8],"by":[9],"employing":[10],"a":[11,40,51],"generalized":[12,61],"modified":[13,58],"form":[14,59],"of":[15,18,60],"fractional":[16,25,37,62],"integrals":[17],"Riemann-type":[19],"via":[20],"convex":[21,30,42],"functions.":[22],"The":[23],"mean":[24],"inequalities":[26,38],"functions":[28],"with":[29],"absolute":[31],"value":[32],"derivatives":[33],"are":[34,44,48,73],"discovered.":[35],"Hermite\u2013Hadamard-type":[36],"symmetric":[41],"function":[43],"explored.":[45],"These":[46],"results":[47,68],"achieved":[49],"using":[50],"fresh":[52],"and":[53],"innovative":[54],"methodology":[55],"integrals.":[63],"Some":[64],"applications":[65],"explored":[69],"in":[70],"paper":[72],"briefly":[74],"reviewed.":[75]},"counts_by_year":[{"year":2025,"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"}
