{"id":"https://openalex.org/W3215443040","doi":"https://doi.org/10.3390/sym13112209","title":"Some Hermite\u2013Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings","display_name":"Some Hermite\u2013Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings","publication_year":2021,"publication_date":"2021-11-19","ids":{"openalex":"https://openalex.org/W3215443040","doi":"https://doi.org/10.3390/sym13112209","mag":"3215443040"},"language":"en","primary_location":{"id":"doi:10.3390/sym13112209","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112209","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2209/pdf?version=1637316423","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/2073-8994/13/11/2209/pdf?version=1637316423","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035042448","display_name":"Soubhagya Kumar Sahoo","orcid":"https://orcid.org/0000-0003-4524-1951"},"institutions":[{"id":"https://openalex.org/I193073490","display_name":"Siksha O Anusandhan University","ror":"https://ror.org/056ep7w45","country_code":"IN","type":"education","lineage":["https://openalex.org/I193073490"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Soubhagya Kumar Sahoo","raw_affiliation_strings":["Department of Mathematics, Institute of Technical Education and Research, Siksha \u2018O\u2019 Anusandhan University, Bhubaneswar 751030, India","Department of Mathematics, Institute of Technical Education and Research, Siksha 'O' Anusandhan University, Bhubaneswar 751030, India"],"raw_orcid":"https://orcid.org/0000-0003-4524-1951","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Institute of Technical Education and Research, Siksha \u2018O\u2019 Anusandhan University, Bhubaneswar 751030, India","institution_ids":["https://openalex.org/I193073490"]},{"raw_affiliation_string":"Department of Mathematics, Institute of Technical Education and Research, Siksha 'O' Anusandhan University, Bhubaneswar 751030, India","institution_ids":["https://openalex.org/I193073490"]}]},{"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"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Tariq","raw_affiliation_strings":["Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-8372-2532","affiliations":[{"raw_affiliation_string":"Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan","institution_ids":["https://openalex.org/I180291457"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114376646","display_name":"Hijaz Ahmad","orcid":"https://orcid.org/0000-0002-5438-5407"},"institutions":[{"id":"https://openalex.org/I4210104933","display_name":"Biruni University","ror":"https://ror.org/01nkhmn89","country_code":"TR","type":"education","lineage":["https://openalex.org/I4210104933"]},{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]}],"countries":["IT","TR"],"is_corresponding":true,"raw_author_name":"Hijaz Ahmad","raw_affiliation_strings":["Department of Computer Engineering, Biruni University, Istanbul 34025, Turkey","Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy"],"raw_orcid":"https://orcid.org/0000-0002-5438-5407","affiliations":[{"raw_affiliation_string":"Department of Computer Engineering, Biruni University, Istanbul 34025, Turkey","institution_ids":["https://openalex.org/I4210104933"]},{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy","institution_ids":["https://openalex.org/I4210155399"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080090568","display_name":"Ayman A. Aly","orcid":"https://orcid.org/0000-0002-8383-8014"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ayman A. Aly","raw_affiliation_strings":["Department of Mechanical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033059507","display_name":"Bassem F. Felemban","orcid":"https://orcid.org/0000-0003-0196-0209"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Bassem F. Felemban","raw_affiliation_strings":["Department of Mechanical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-0196-0209","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031839753","display_name":"Phatiphat Thounthong","orcid":"https://orcid.org/0000-0002-1453-4236"},"institutions":[{"id":"https://openalex.org/I82828225","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97","country_code":"TH","type":"education","lineage":["https://openalex.org/I82828225"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Phatiphat Thounthong","raw_affiliation_strings":["Renewable Energy Research Centre (RERC), Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","Renewable Energy Research Centre (RERC), Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand"],"raw_orcid":"https://orcid.org/0000-0002-1453-4236","affiliations":[{"raw_affiliation_string":"Renewable Energy Research Centre (RERC), Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]},{"raw_affiliation_string":"Renewable Energy Research Centre (RERC), Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]}]}],"institutions":[],"countries_distinct_count":6,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5071660334","https://openalex.org/A5114376646"],"corresponding_institution_ids":["https://openalex.org/I180291457","https://openalex.org/I4210104933","https://openalex.org/I4210155399"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":3.195,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.92924427,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"13","issue":"11","first_page":"2209","last_page":"2209"},"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":0.9532999992370605,"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":0.9441999793052673,"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/differentiable-function","display_name":"Differentiable function","score":0.7420699596405029},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6860981583595276},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5987805724143982},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.5478373765945435},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5106115937232971},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.49330654740333557},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.4909079670906067},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.46490347385406494},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44644099473953247},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.43663516640663147},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.42476195096969604},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.34655383229255676},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3457072973251343},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33890441060066223},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.2801045775413513}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.7420699596405029},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6860981583595276},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5987805724143982},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.5478373765945435},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5106115937232971},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.49330654740333557},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.4909079670906067},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.46490347385406494},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44644099473953247},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.43663516640663147},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.42476195096969604},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.34655383229255676},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3457072973251343},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33890441060066223},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2801045775413513},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym13112209","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112209","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2209/pdf?version=1637316423","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:d9abdd6353064fe0a1feea967f9b8f6a","is_oa":true,"landing_page_url":"https://doaj.org/article/d9abdd6353064fe0a1feea967f9b8f6a","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 13, Iss 11, p 2209 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/11/2209/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13112209","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"},{"id":"pmh:oai:zenodo.org:176456","is_oa":true,"landing_page_url":"https://www.openaccessrepository.it/record/176456","pdf_url":null,"source":{"id":"https://openalex.org/S4306402478","display_name":"INFM-OAR (INFN Catania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210116497","host_organization_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Catania","host_organization_lineage":["https://openalex.org/I4210116497"],"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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/sym13112209","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112209","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2209/pdf?version=1637316423","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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3215443040.pdf"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1989479808","https://openalex.org/W1992131688","https://openalex.org/W2006458314","https://openalex.org/W2017682769","https://openalex.org/W2032988465","https://openalex.org/W2033721561","https://openalex.org/W2049888876","https://openalex.org/W2054288497","https://openalex.org/W2057807431","https://openalex.org/W2060339799","https://openalex.org/W2087320643","https://openalex.org/W2108938561","https://openalex.org/W2127403683","https://openalex.org/W2322767775","https://openalex.org/W2519050643","https://openalex.org/W2962519699","https://openalex.org/W2983913010","https://openalex.org/W3020810561","https://openalex.org/W3031981046","https://openalex.org/W3035567448","https://openalex.org/W3043710525","https://openalex.org/W3045812442","https://openalex.org/W3046588138","https://openalex.org/W3083821625","https://openalex.org/W3085558482","https://openalex.org/W3086959608","https://openalex.org/W3087236563","https://openalex.org/W3088317680","https://openalex.org/W3093285267","https://openalex.org/W3093309257","https://openalex.org/W3096393371","https://openalex.org/W3097528563","https://openalex.org/W3114933723","https://openalex.org/W3132844534","https://openalex.org/W3135781820","https://openalex.org/W3165575330","https://openalex.org/W3179403041","https://openalex.org/W3197580818","https://openalex.org/W3202656222","https://openalex.org/W4292070096","https://openalex.org/W6735250351","https://openalex.org/W6792195833","https://openalex.org/W6798611357","https://openalex.org/W6802173645"],"related_works":["https://openalex.org/W4396753818","https://openalex.org/W1996226968","https://openalex.org/W4294618985","https://openalex.org/W2518252082","https://openalex.org/W2364547801","https://openalex.org/W4398758929","https://openalex.org/W257189624","https://openalex.org/W2393350255","https://openalex.org/W2788930696","https://openalex.org/W4301016436"],"abstract_inverted_index":{"The":[0,69],"theory":[1,42],"of":[2,10,43,53,59,71,104,111,132],"fractional":[3,44,85],"analysis":[4],"has":[5],"been":[6],"a":[7,148],"focal":[8],"point":[9],"fascination":[11],"for":[12,108],"scientists":[13],"in":[14,24,40,55,63,141,144],"mathematical":[15],"science,":[16],"given":[17],"its":[18,88],"essential":[19],"definitions,":[20],"properties,":[21],"and":[22,46,67,87,135],"applications":[23,54,140],"handling":[25],"real-life":[26],"problems.":[27],"In":[28],"the":[29,41,83,125,136],"last":[30],"few":[31],"decades,":[32],"many":[33],"mathematicians":[34],"have":[35,139],"shown":[36],"their":[37,50],"considerable":[38],"interest":[39],"calculus":[45],"convexity":[47],"due":[48],"to":[49,75,123],"wide":[51],"range":[52],"almost":[56],"all":[57],"branches":[58],"applied":[60,122],"sciences,":[61],"especially":[62],"numerical":[64],"analysis,":[65],"physics,":[66],"engineering.":[68],"objective":[70],"this":[72,133],"article":[73],"is":[74],"establish":[76],"Hermite-Hadamard":[77],"type":[78],"integral":[79,130],"inequalities":[80,131],"by":[81],"employing":[82],"k-Riemann-Liouville":[84],"operator":[86],"refinements,":[89],"whose":[90],"absolute":[91],"values":[92],"are":[93],"twice-differentiable":[94],"h-convex":[95],"functions.":[96],"Moreover,":[97,113],"we":[98,114],"also":[99,115],"present":[100],"some":[101],"special":[102],"cases":[103],"our":[105],"presented":[106],"results":[107],"different":[109],"types":[110],"convexities.":[112],"study":[116],"how":[117],"q-digamma":[118],"functions":[119],"can":[120],"be":[121],"address":[124],"newly":[126],"investigated":[127],"results.":[128],"Mathematical":[129],"class":[134],"arrangements":[137],"associated":[138],"diverse":[142],"domains":[143],"which":[145],"symmetry":[146],"presents":[147],"salient":[149],"role.":[150]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
