{"id":"https://openalex.org/W4362669707","doi":"https://doi.org/10.3390/sym15040868","title":"Some New Hermite\u2013Hadamard Type Inequalities Pertaining to Generalized Multiplicative Fractional Integrals","display_name":"Some New Hermite\u2013Hadamard Type Inequalities Pertaining to Generalized Multiplicative Fractional Integrals","publication_year":2023,"publication_date":"2023-04-05","ids":{"openalex":"https://openalex.org/W4362669707","doi":"https://doi.org/10.3390/sym15040868"},"language":"en","primary_location":{"id":"doi:10.3390/sym15040868","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040868","pdf_url":"https://www.mdpi.com/2073-8994/15/4/868/pdf?version=1680751387","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/2073-8994/15/4/868/pdf?version=1680751387","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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 and Natural Sciences, University \u201cIsmail Qemali\u201d, 9400 Vlora, Albania","Department of Mathematics, Faculty of Technical and Natural Sciences, University \"Ismail Qemali\", 9400 Vlora, Albania"],"raw_orcid":"https://orcid.org/0000-0003-0115-3079","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Technical and Natural Sciences, University \u201cIsmail Qemali\u201d, 9400 Vlora, Albania","institution_ids":["https://openalex.org/I3130420675"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Technical and Natural Sciences, University \"Ismail Qemali\", 9400 Vlora, Albania","institution_ids":["https://openalex.org/I3130420675"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035042448","display_name":"Soubhagya Kumar Sahoo","orcid":"https://orcid.org/0000-0003-4524-1951"},"institutions":[{"id":"https://openalex.org/I4210125057","display_name":"Vivekananda Global University","ror":"https://ror.org/038mz4r36","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210125057"]},{"id":"https://openalex.org/I4387930198","display_name":"C.V. Raman Global University","ror":"https://ror.org/032583b91","country_code":null,"type":"education","lineage":["https://openalex.org/I4387930198"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Soubhagya Kumar Sahoo","raw_affiliation_strings":["Department of Mathematics, C.V. Raman Global University, Bhubaneswar 752054, India"],"raw_orcid":"https://orcid.org/0000-0003-4524-1951","affiliations":[{"raw_affiliation_string":"Department of Mathematics, C.V. Raman Global University, Bhubaneswar 752054, India","institution_ids":["https://openalex.org/I4210125057","https://openalex.org/I4387930198"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052556999","display_name":"Munirah Aljuaid","orcid":"https://orcid.org/0000-0002-5748-9738"},"institutions":[{"id":"https://openalex.org/I118590987","display_name":"Northern Border University","ror":"https://ror.org/03j9tzj20","country_code":"SA","type":"education","lineage":["https://openalex.org/I118590987"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Munirah Aljuaid","raw_affiliation_strings":["Department of Mathematics, College of Science, Northern Border University, Arar 73213, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-5748-9738","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Northern Border University, Arar 73213, Saudi Arabia","institution_ids":["https://openalex.org/I118590987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071660334","display_name":"Muhammad Tariq","orcid":"https://orcid.org/0000-0001-8372-2532"},"institutions":[{"id":"https://openalex.org/I180291457","display_name":"Mehran University of Engineering and Technology","ror":"https://ror.org/0575ttm03","country_code":"PK","type":"education","lineage":["https://openalex.org/I180291457"]},{"id":"https://openalex.org/I20561161","display_name":"University of Balochistan","ror":"https://ror.org/04bf33n91","country_code":"PK","type":"education","lineage":["https://openalex.org/I20561161"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Tariq","raw_affiliation_strings":["Department of Basic Sciences and Related Studies, Mehran UET, Jamshoro 76062, Pakistan","Department of Mathematics, Balochistan Residential College, Loralai 84800, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-8372-2532","affiliations":[{"raw_affiliation_string":"Department of Basic Sciences and Related Studies, Mehran UET, Jamshoro 76062, Pakistan","institution_ids":["https://openalex.org/I180291457"]},{"raw_affiliation_string":"Department of Mathematics, Balochistan Residential College, Loralai 84800, Pakistan","institution_ids":["https://openalex.org/I20561161"]}]},{"author_position":"last","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":["Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of Basque Country, 48940 Leioa, Spain"],"raw_orcid":"https://orcid.org/0000-0001-9320-9433","affiliations":[{"raw_affiliation_string":"Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of Basque Country, 48940 Leioa, Spain","institution_ids":["https://openalex.org/I169108374"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5035042448","https://openalex.org/A5042326806"],"corresponding_institution_ids":["https://openalex.org/I169108374","https://openalex.org/I4210125057","https://openalex.org/I4387930198"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":13.9761,"has_fulltext":true,"cited_by_count":28,"citation_normalized_percentile":{"value":0.99678653,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"15","issue":"4","first_page":"868","last_page":"868"},"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":0.9718999862670898,"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":0.9544000029563904,"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/multiplicative-function","display_name":"Multiplicative function","score":0.8604470491409302},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.782745361328125},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6241630911827087},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.555698037147522},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.5481992363929749},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5191518664360046},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.49178364872932434},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.45873749256134033},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.45210808515548706},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4454701840877533},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41335296630859375},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4132745862007141},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24178281426429749},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0669792890548706}],"concepts":[{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.8604470491409302},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.782745361328125},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6241630911827087},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.555698037147522},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.5481992363929749},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5191518664360046},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.49178364872932434},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.45873749256134033},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.45210808515548706},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4454701840877533},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41335296630859375},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4132745862007141},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24178281426429749},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0669792890548706},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym15040868","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040868","pdf_url":"https://www.mdpi.com/2073-8994/15/4/868/pdf?version=1680751387","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:10810/60980","is_oa":true,"landing_page_url":"http://hdl.handle.net/10810/60980","pdf_url":"http://addi.ehu.es/bitstream/10810/60980/1/symmetry-15-00868-v2.pdf","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:b555b0610adb4fdaab6f6fd3539be8ad","is_oa":false,"landing_page_url":"https://doaj.org/article/b555b0610adb4fdaab6f6fd3539be8ad","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 15, Iss 4, p 868 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/4/868/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15040868","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/sym15040868","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040868","pdf_url":"https://www.mdpi.com/2073-8994/15/4/868/pdf?version=1680751387","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":0.6399999856948853,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G1812785629","display_name":null,"funder_award_id":"PID2021-1235430B-C21","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"},{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G300979063","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3497146170","display_name":null,"funder_award_id":"IT1555-22","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"},{"id":"https://openalex.org/G5080475149","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7266728691","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7922698992","display_name":null,"funder_award_id":"KK-2022/00090","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"}],"funders":[{"id":"https://openalex.org/F4320321705","display_name":"Eusko Jaurlaritza","ror":"https://ror.org/00pz2fp31"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4362669707.pdf"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W816848581","https://openalex.org/W1976054910","https://openalex.org/W1978037192","https://openalex.org/W1997069243","https://openalex.org/W2006458314","https://openalex.org/W2143105934","https://openalex.org/W2304758964","https://openalex.org/W2519050643","https://openalex.org/W2570306563","https://openalex.org/W2736167298","https://openalex.org/W2777975310","https://openalex.org/W2793326209","https://openalex.org/W2794131076","https://openalex.org/W2801192398","https://openalex.org/W2917597246","https://openalex.org/W2940692662","https://openalex.org/W2945222953","https://openalex.org/W2947646583","https://openalex.org/W2965670039","https://openalex.org/W2972125909","https://openalex.org/W2999051718","https://openalex.org/W3015825894","https://openalex.org/W3025078896","https://openalex.org/W3034824543","https://openalex.org/W3036009238","https://openalex.org/W3037345886","https://openalex.org/W3038745701","https://openalex.org/W3045610251","https://openalex.org/W3094365264","https://openalex.org/W3107166052","https://openalex.org/W3135781820","https://openalex.org/W3161184056","https://openalex.org/W3163847978","https://openalex.org/W4205475114","https://openalex.org/W4214911527","https://openalex.org/W4221089321","https://openalex.org/W4221110719","https://openalex.org/W4224286022","https://openalex.org/W4225002616","https://openalex.org/W4225881010","https://openalex.org/W4288052931","https://openalex.org/W4295836062","https://openalex.org/W4295886878","https://openalex.org/W4297238086","https://openalex.org/W4312204258","https://openalex.org/W4312204988","https://openalex.org/W4312910258","https://openalex.org/W4313531098","https://openalex.org/W6698366594","https://openalex.org/W6777593310","https://openalex.org/W6780276795","https://openalex.org/W6792195833"],"related_works":["https://openalex.org/W4396753818","https://openalex.org/W4210791199","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","https://openalex.org/W4206205240"],"abstract_inverted_index":{"There":[0],"is":[1,21,29],"significant":[2],"interaction":[3],"between":[4],"the":[5,25,84,97],"class":[6],"of":[7,13,27,31,59,87,99],"symmetric":[8],"functions":[9,49,64,90],"and":[10,50,91],"other":[11],"types":[12],"functions.":[14],"The":[15],"multiplicative":[16,41,47,62,68,88],"convex":[17,48,63,89],"function":[18],"class,":[19],"which":[20],"intimately":[22],"related":[23,65],"to":[24,66,95],"idea":[26],"symmetry,":[28],"one":[30],"them.":[32],"In":[33],"this":[34],"paper,":[35],"we":[36,55],"obtain":[37],"some":[38,81],"new":[39],"generalized":[40,67],"fractional":[42,69],"Hermite\u2013Hadamard":[43],"type":[44],"inequalities":[45,60],"for":[46,51,61,83],"their":[52,92],"product.":[53],"Additionally,":[54],"derive":[56],"a":[57,72],"number":[58],"integrals":[70],"utilising":[71],"novel":[73],"identity":[74],"as":[75],"an":[76],"auxiliary":[77],"result.":[78],"We":[79],"provide":[80],"examples":[82],"appropriate":[85],"selections":[86],"graphical":[93],"representations":[94],"verify":[96],"authenticity":[98],"our":[100],"main":[101],"results.":[102]},"counts_by_year":[{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":3}],"updated_date":"2026-05-31T08:46:17.908082","created_date":"2025-10-10T00:00:00"}