{"id":"https://openalex.org/W4293770955","doi":"https://doi.org/10.3390/sym14091774","title":"Hermite\u2013Hadamard-Type Inequalities Involving Harmonically Convex Function via the Atangana\u2013Baleanu Fractional Integral Operator","display_name":"Hermite\u2013Hadamard-Type Inequalities Involving Harmonically Convex Function via the Atangana\u2013Baleanu Fractional Integral Operator","publication_year":2022,"publication_date":"2022-08-25","ids":{"openalex":"https://openalex.org/W4293770955","doi":"https://doi.org/10.3390/sym14091774"},"language":"en","primary_location":{"id":"doi:10.3390/sym14091774","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091774","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1774/pdf?version=1661419604","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/2073-8994/14/9/1774/pdf?version=1661419604","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007747705","display_name":"Muhammad Amer Latif","orcid":"https://orcid.org/0000-0003-2349-3445"},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Muhammad Amer Latif","raw_affiliation_strings":["Department of Basic Sciences, King Faisal University, Hofuf 31982, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-2349-3445","affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, King Faisal University, Hofuf 31982, Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001569809","display_name":"Humaira Kalsoom","orcid":"https://orcid.org/0000-0002-5835-3349"},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Humaira Kalsoom","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China"],"raw_orcid":"https://orcid.org/0000-0002-5835-3349","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China","institution_ids":["https://openalex.org/I135237710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032276471","display_name":"Muhammad Zainul Abidin","orcid":"https://orcid.org/0000-0001-8567-0676"},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Muhammad Zainul Abidin","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China"],"raw_orcid":"https://orcid.org/0000-0001-8567-0676","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China","institution_ids":["https://openalex.org/I135237710"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001569809","https://openalex.org/A5032276471"],"corresponding_institution_ids":["https://openalex.org/I135237710"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.5579,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.93613206,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"14","issue":"9","first_page":"1774","last_page":"1774"},"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":0.9722999930381775,"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":0.9423999786376953,"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":0.7857173681259155},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.6962429881095886},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.6831908226013184},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6112630367279053},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5675109028816223},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5443704724311829},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5251013040542603},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43172433972358704},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4141119122505188},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4001847207546234},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.382470041513443},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3371293842792511}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7857173681259155},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.6962429881095886},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.6831908226013184},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6112630367279053},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5675109028816223},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5443704724311829},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5251013040542603},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43172433972358704},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4141119122505188},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4001847207546234},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.382470041513443},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3371293842792511},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14091774","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091774","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1774/pdf?version=1661419604","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:69382843393d4a5bbfe1e02a82467b02","is_oa":true,"landing_page_url":"https://doaj.org/article/69382843393d4a5bbfe1e02a82467b02","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 9, p 1774 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/9/1774/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14091774","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; Volume 14; Issue 9; Pages: 1774","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14091774","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091774","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1774/pdf?version=1661419604","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","id":"https://metadata.un.org/sdg/10","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4293770955.pdf","grobid_xml":"https://content.openalex.org/works/W4293770955.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W1499929944","https://openalex.org/W1515819310","https://openalex.org/W1579472190","https://openalex.org/W1990485388","https://openalex.org/W1994050833","https://openalex.org/W1995366777","https://openalex.org/W2006458314","https://openalex.org/W2056135743","https://openalex.org/W2060208030","https://openalex.org/W2072882480","https://openalex.org/W2097184643","https://openalex.org/W2117331148","https://openalex.org/W2469986892","https://openalex.org/W2520410115","https://openalex.org/W2556784265","https://openalex.org/W2905702751","https://openalex.org/W2907206424","https://openalex.org/W2945746308","https://openalex.org/W2949130693","https://openalex.org/W2963641381","https://openalex.org/W2963951848","https://openalex.org/W2964046643","https://openalex.org/W3000320805","https://openalex.org/W3001262513","https://openalex.org/W3009949796","https://openalex.org/W3015640008","https://openalex.org/W3015825894","https://openalex.org/W3024628904","https://openalex.org/W3029739835","https://openalex.org/W3032034118","https://openalex.org/W3037530917","https://openalex.org/W3038745701","https://openalex.org/W3043212253","https://openalex.org/W3044973613","https://openalex.org/W3045812442","https://openalex.org/W3083821625","https://openalex.org/W3098627266","https://openalex.org/W3114933723","https://openalex.org/W3164562742","https://openalex.org/W3171223766","https://openalex.org/W3176364078","https://openalex.org/W4240615911","https://openalex.org/W6630032168","https://openalex.org/W6647817991","https://openalex.org/W6725866017","https://openalex.org/W6730176618","https://openalex.org/W6771554700","https://openalex.org/W6780276795"],"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":{"Fractional":[0],"integrals":[1],"and":[2,9,34,52,78,117],"inequalities":[3,25,38,63,94,116],"have":[4,10,26,95],"recently":[5],"become":[6],"quite":[7],"popular":[8],"been":[11,27,96],"the":[12,85,110],"prime":[13],"consideration":[14],"for":[15,74,101],"many":[16,21,123],"studies.":[17],"The":[18,91],"results":[19],"of":[20,24,61,64,84,104,112],"different":[22],"types":[23],"studied":[28],"by":[29],"launching":[30],"innovative":[31],"analytical":[32],"techniques":[33],"applications.":[35],"These":[36],"Hermite\u2013Hadamard":[37,65],"are":[39,120],"discovered":[40],"in":[41,122],"this":[42,56],"study":[43,60],"using":[44,79],"Atangana\u2013Baleanu":[45,75],"integral":[46,62,76],"operators,":[47],"which":[48],"provide":[49],"both":[50],"practical":[51],"powerful":[53],"results.":[54],"In":[55],"paper,":[57],"a":[58,102],"symmetric":[59],"type":[66],"is":[67,88],"provided":[68],"based":[69],"on":[70],"an":[71],"identity":[72],"proved":[73],"operators":[77],"functions":[80],"whose":[81],"absolute":[82],"value":[83],"second":[86],"derivative":[87],"harmonic":[89,106],"convex.":[90],"proven":[92],"Hermite\u2013Hadamard-type":[93],"observed":[97],"to":[98],"be":[99],"valid":[100],"choice":[103],"any":[105],"convex":[107],"function":[108],"with":[109],"help":[111],"examples.":[113],"Moreover,":[114],"fractional":[115],"their":[118],"solutions":[119],"applied":[121],"symmetrical":[124],"domains.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
