{"id":"https://openalex.org/W4296745895","doi":"https://doi.org/10.3390/sym14101957","title":"Some Hermite\u2013Hadamard and Hermite\u2013Hadamard\u2013Fej\u00e9r Type Fractional Inclusions Pertaining to Different Kinds of Generalized Preinvexities","display_name":"Some Hermite\u2013Hadamard and Hermite\u2013Hadamard\u2013Fej\u00e9r Type Fractional Inclusions Pertaining to Different Kinds of Generalized Preinvexities","publication_year":2022,"publication_date":"2022-09-20","ids":{"openalex":"https://openalex.org/W4296745895","doi":"https://doi.org/10.3390/sym14101957"},"language":"en","primary_location":{"id":"doi:10.3390/sym14101957","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14101957","pdf_url":"https://www.mdpi.com/2073-8994/14/10/1957/pdf?version=1666268593","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/2073-8994/14/10/1957/pdf?version=1666268593","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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":false,"raw_author_name":"Muhammad Tariq","raw_affiliation_strings":["Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan"],"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/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, Aryan Institute of Engineering and Technology, Bhubaneswar 752050, India","Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar 751030, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Aryan Institute of Engineering and Technology, Bhubaneswar 752050, India","institution_ids":[]},{"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/A5086599287","display_name":"Sotiris K. Ntouyas","orcid":"https://orcid.org/0000-0002-7695-2118"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]},{"id":"https://openalex.org/I194019607","display_name":"University of Ioannina","ror":"https://ror.org/01qg3j183","country_code":"GR","type":"education","lineage":["https://openalex.org/I194019607"]}],"countries":["GR","SA"],"is_corresponding":false,"raw_author_name":"Sotiris K. Ntouyas","raw_affiliation_strings":["Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece","Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece","institution_ids":["https://openalex.org/I194019607"]},{"raw_affiliation_string":"Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048951363","display_name":"Omar Mutab Alsalami","orcid":"https://orcid.org/0000-0001-7530-6264"},"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":"Omar Mutab Alsalami","raw_affiliation_strings":["Department of Electrical Engineering, College of Engineering, Taif University, Taif 21944, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, College of Engineering, Taif University, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080183718","display_name":"Asif Ali Shaikh","orcid":"https://orcid.org/0000-0002-3084-922X"},"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":false,"raw_author_name":"Asif Ali Shaikh","raw_affiliation_strings":["Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan"],"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":"last","author":{"id":"https://openalex.org/A5089496116","display_name":"Kamsing Nonlaopon","orcid":"https://orcid.org/0000-0002-7469-5402"},"institutions":[{"id":"https://openalex.org/I179193067","display_name":"Khon Kaen University","ror":"https://ror.org/03cq4gr50","country_code":"TH","type":"education","lineage":["https://openalex.org/I179193067"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Kamsing Nonlaopon","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand","institution_ids":["https://openalex.org/I179193067"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5089496116"],"corresponding_institution_ids":["https://openalex.org/I179193067"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.7577,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.83889327,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"14","issue":"10","first_page":"1957","last_page":"1957"},"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":0.9574999809265137,"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":0.9520999789237976,"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/hadamard-transform","display_name":"Hadamard transform","score":0.8140653371810913},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7417107224464417},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.6952455043792725},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.680797815322876},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6246996521949768},{"id":"https://openalex.org/keywords/conformable-matrix","display_name":"Conformable matrix","score":0.6157135367393494},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5744271874427795},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5604286193847656},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5464289784431458},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45527830719947815},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.4235530197620392},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32233095169067383},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06227949261665344}],"concepts":[{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.8140653371810913},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7417107224464417},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.6952455043792725},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.680797815322876},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6246996521949768},{"id":"https://openalex.org/C86072612","wikidata":"https://www.wikidata.org/wiki/Q5160239","display_name":"Conformable matrix","level":2,"score":0.6157135367393494},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5744271874427795},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5604286193847656},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5464289784431458},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45527830719947815},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.4235530197620392},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32233095169067383},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06227949261665344},{"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14101957","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14101957","pdf_url":"https://www.mdpi.com/2073-8994/14/10/1957/pdf?version=1666268593","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:488b96703ab143fd9ba5260795030228","is_oa":true,"landing_page_url":"https://doaj.org/article/488b96703ab143fd9ba5260795030228","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 10, p 1957 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/10/1957/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14101957","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/sym14101957","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14101957","pdf_url":"https://www.mdpi.com/2073-8994/14/10/1957/pdf?version=1666268593","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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.7099999785423279}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4296745895.pdf","grobid_xml":"https://content.openalex.org/works/W4296745895.grobid-xml"},"referenced_works_count":64,"referenced_works":["https://openalex.org/W611121171","https://openalex.org/W1492900090","https://openalex.org/W1542307911","https://openalex.org/W1548897287","https://openalex.org/W1753677234","https://openalex.org/W1969573529","https://openalex.org/W1974271314","https://openalex.org/W1975875076","https://openalex.org/W1987344300","https://openalex.org/W1988180087","https://openalex.org/W1990037710","https://openalex.org/W2000983337","https://openalex.org/W2006458314","https://openalex.org/W2010387581","https://openalex.org/W2012192004","https://openalex.org/W2019573725","https://openalex.org/W2046396733","https://openalex.org/W2063067239","https://openalex.org/W2082777487","https://openalex.org/W2094786643","https://openalex.org/W2103233901","https://openalex.org/W2137618609","https://openalex.org/W2161011292","https://openalex.org/W2318304944","https://openalex.org/W2318890204","https://openalex.org/W2344995561","https://openalex.org/W2496776199","https://openalex.org/W2519050643","https://openalex.org/W2743775362","https://openalex.org/W2772643525","https://openalex.org/W2790996674","https://openalex.org/W2802275298","https://openalex.org/W2907252008","https://openalex.org/W2909768556","https://openalex.org/W2949130693","https://openalex.org/W2971601979","https://openalex.org/W3012221704","https://openalex.org/W3014866661","https://openalex.org/W3035325981","https://openalex.org/W3036939179","https://openalex.org/W3042754882","https://openalex.org/W3049332307","https://openalex.org/W3087013225","https://openalex.org/W3089415942","https://openalex.org/W3103583610","https://openalex.org/W3116401574","https://openalex.org/W3133766583","https://openalex.org/W3162607444","https://openalex.org/W4200119862","https://openalex.org/W4205249021","https://openalex.org/W4205326909","https://openalex.org/W4221089321","https://openalex.org/W4285240662","https://openalex.org/W6632705453","https://openalex.org/W6648694050","https://openalex.org/W6683553287","https://openalex.org/W6724268012","https://openalex.org/W6733656844","https://openalex.org/W6754271363","https://openalex.org/W6757351614","https://openalex.org/W6758695705","https://openalex.org/W6779139925","https://openalex.org/W6787829078","https://openalex.org/W6884957409"],"related_works":["https://openalex.org/W3158217983","https://openalex.org/W4248103533","https://openalex.org/W3046588275","https://openalex.org/W3085259849","https://openalex.org/W2792191619","https://openalex.org/W3046886605","https://openalex.org/W3008631921","https://openalex.org/W4313364931","https://openalex.org/W4302307873","https://openalex.org/W4396753818"],"abstract_inverted_index":{"Fractional":[0],"derivative":[1],"and":[2,30,36,61,74,116],"integral":[3,86],"operators":[4,20],"are":[5,114],"often":[6],"employed":[7],"to":[8,80],"present":[9,90],"new":[10,18,38,115],"generalizations":[11],"of":[12,17,28,52,76,98,118],"mathematical":[13],"inequalities.":[14],"The":[15,102],"introduction":[16],"fractional":[19,39,70,85],"has":[21],"prompted":[22],"another":[23],"direction":[24],"in":[25,111],"different":[26],"branches":[27],"mathematics":[29],"applied":[31],"sciences.":[32],"First,":[33],"we":[34,48,67,89],"investigate":[35,68],"prove":[37],"equality.":[40],"Considering":[41],"this":[42,112],"equality":[43],"as":[44,104,106],"the":[45,96,107],"auxiliary":[46],"result,":[47],"attain":[49],"some":[50,75],"estimations":[51],"a":[53,69,83,91],"Hermite\u2013Hadamard":[54],"type":[55,93],"inequality":[56,73,94],"involving":[57],"s-preinvex,":[58],"s-Godunova\u2013Levin":[59],"preinvex,":[60],"prequasi":[62],"invex":[63],"functions.":[64,101],"In":[65],"addition,":[66],"order":[71],"Hadamard\u2013Fej\u00e9r":[72],"its":[77],"refinements":[78],"pertaining":[79],"h-preinvexity":[81],"via":[82],"non-conformable":[84],"operator.":[87],"Finally,":[88],"Pachpatte":[92],"for":[95],"product":[97],"two":[99],"preinvex":[100],"findings":[103],"well":[105],"special":[108],"cases":[109],"presented":[110],"research":[113],"applications":[117],"our":[119],"main":[120],"results.":[121]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-09-23T00:00:00"}
