{"id":"https://openalex.org/W4205475114","doi":"https://doi.org/10.1007/s44196-021-00061-6","title":"Hermite\u2013Hadamard Type Inequalities for Interval-Valued Preinvex Functions via Fractional Integral Operators","display_name":"Hermite\u2013Hadamard Type Inequalities for Interval-Valued Preinvex Functions via Fractional Integral Operators","publication_year":2022,"publication_date":"2022-01-19","ids":{"openalex":"https://openalex.org/W4205475114","doi":"https://doi.org/10.1007/s44196-021-00061-6"},"language":"en","primary_location":{"id":"doi:10.1007/s44196-021-00061-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-021-00061-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-021-00061-6.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007/s44196-021-00061-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079512627","display_name":"H. M. Srivastava","orcid":"https://orcid.org/0000-0002-9277-8092"},"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/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]},{"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/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]},{"id":"https://openalex.org/I87490745","display_name":"Azerbaijan University","ror":"https://ror.org/00g1psz15","country_code":"AZ","type":"education","lineage":["https://openalex.org/I87490745"]}],"countries":["AZ","CA","IT","TW"],"is_corresponding":false,"raw_author_name":"Hari Mohan Srivastava","raw_affiliation_strings":["Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007, Baku, Azerbaijan","Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada","Department of Medical Research, China Medical University Hospital, China Medical University, Taizhong, 40402, Taiwan, Republic of China","Section of Mathematics, International Telematic University Uninettuno, 00186, Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0002-9277-8092","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007, Baku, Azerbaijan","institution_ids":["https://openalex.org/I87490745"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada","institution_ids":["https://openalex.org/I212119943"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University Hospital, China Medical University, Taizhong, 40402, Taiwan, Republic of China","institution_ids":["https://openalex.org/I184693016","https://openalex.org/I4210126829"]},{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, 00186, Rome, Italy","institution_ids":["https://openalex.org/I4210155399"]}]},{"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, Siksha O Anusandhan University, Bhubaneswar, Odisha, 751030, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Siksha O Anusandhan University, Bhubaneswar, Odisha, 751030, India","institution_ids":["https://openalex.org/I193073490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059025015","display_name":"Pshtiwan Othman Mohammed","orcid":"https://orcid.org/0000-0001-6837-8075"},"institutions":[{"id":"https://openalex.org/I64952554","display_name":"University of Sulaimani","ror":"https://ror.org/00saanr69","country_code":"IQ","type":"education","lineage":["https://openalex.org/I64952554"]}],"countries":["IQ"],"is_corresponding":true,"raw_author_name":"Pshtiwan Othman Mohammed","raw_affiliation_strings":["Department of Mathematics, College of Education, University of Sulaimani, Kurdistan Region, Sulaymaniyah, Iraq"],"raw_orcid":"https://orcid.org/0000-0001-6837-8075","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Education, University of Sulaimani, Kurdistan Region, Sulaymaniyah, Iraq","institution_ids":["https://openalex.org/I64952554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030756029","display_name":"Dumitru B\u01celeanu","orcid":"https://orcid.org/0000-0002-0286-7244"},"institutions":[{"id":"https://openalex.org/I106245021","display_name":"\u00c7ankaya University","ror":"https://ror.org/056wqre19","country_code":"TR","type":"education","lineage":["https://openalex.org/I106245021"]},{"id":"https://openalex.org/I4210142834","display_name":"Institute of Space Science - INFLPR Subsidiary","ror":"https://ror.org/054a6wv56","country_code":"RO","type":"facility","lineage":["https://openalex.org/I4210142834"]}],"countries":["RO","TR"],"is_corresponding":true,"raw_author_name":"Dumitru Baleanu","raw_affiliation_strings":["Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey","Institute of Space Sciences, P.O. Box, MG-23, Magurele-Bucharest, 76900, M\u0103gurele, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey","institution_ids":["https://openalex.org/I106245021"]},{"raw_affiliation_string":"Institute of Space Sciences, P.O. Box, MG-23, Magurele-Bucharest, 76900, M\u0103gurele, Romania","institution_ids":["https://openalex.org/I4210142834"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050299764","display_name":"Bibhakar Kodamasingh","orcid":"https://orcid.org/0000-0002-2751-7793"},"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":"Bibhakar Kodamasingh","raw_affiliation_strings":["Department of Mathematics, Siksha O Anusandhan University, Bhubaneswar, Odisha, 751030, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Siksha O Anusandhan University, Bhubaneswar, Odisha, 751030, India","institution_ids":["https://openalex.org/I193073490"]}]}],"institutions":[],"countries_distinct_count":8,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5030756029","https://openalex.org/A5059025015"],"corresponding_institution_ids":["https://openalex.org/I106245021","https://openalex.org/I4210142834","https://openalex.org/I64952554"],"apc_list":{"value":1390,"currency":"GBP","value_usd":1704},"apc_paid":{"value":1390,"currency":"GBP","value_usd":1704},"fwci":16.0003,"has_fulltext":true,"cited_by_count":46,"citation_normalized_percentile":{"value":0.99759743,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"15","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9997000098228455,"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":0.9997000098228455,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8338931798934937},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.6915099620819092},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6750675439834595},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.6098257303237915},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5754193067550659},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5132948756217957},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5113017559051514},{"id":"https://openalex.org/keywords/riemann-integral","display_name":"Riemann integral","score":0.4573928117752075},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.45701390504837036},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.4444023072719574},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.441057413816452},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34812837839126587},{"id":"https://openalex.org/keywords/fourier-integral-operator","display_name":"Fourier integral operator","score":0.25447946786880493},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.21820032596588135},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08891656994819641}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8338931798934937},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.6915099620819092},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6750675439834595},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.6098257303237915},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5754193067550659},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5132948756217957},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5113017559051514},{"id":"https://openalex.org/C41833934","wikidata":"https://www.wikidata.org/wiki/Q697181","display_name":"Riemann integral","level":4,"score":0.4573928117752075},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45701390504837036},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.4444023072719574},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.441057413816452},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34812837839126587},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.25447946786880493},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.21820032596588135},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08891656994819641},{"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s44196-021-00061-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-021-00061-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-021-00061-6.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s44196-021-00061-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-021-00061-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-021-00061-6.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5600000023841858,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4205475114.pdf","grobid_xml":"https://content.openalex.org/works/W4205475114.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1969573529","https://openalex.org/W2000983337","https://openalex.org/W2006458314","https://openalex.org/W2012192004","https://openalex.org/W2014526650","https://openalex.org/W2019573725","https://openalex.org/W2053149227","https://openalex.org/W2094786643","https://openalex.org/W2130685476","https://openalex.org/W2556396095","https://openalex.org/W2613734495","https://openalex.org/W2909314559","https://openalex.org/W2913730716","https://openalex.org/W2945033688","https://openalex.org/W2965312062","https://openalex.org/W2982171697","https://openalex.org/W3027817760","https://openalex.org/W3087321204","https://openalex.org/W3105241397","https://openalex.org/W3120114781","https://openalex.org/W3135383876","https://openalex.org/W3163997631","https://openalex.org/W3164799850","https://openalex.org/W3177382062","https://openalex.org/W3180347984","https://openalex.org/W3183326526","https://openalex.org/W3189745929","https://openalex.org/W3201806466","https://openalex.org/W3207265261","https://openalex.org/W3210781357","https://openalex.org/W4212804141"],"related_works":["https://openalex.org/W1982241170","https://openalex.org/W2386549147","https://openalex.org/W1978051046","https://openalex.org/W2950361249","https://openalex.org/W4293557899","https://openalex.org/W2111217632","https://openalex.org/W2960622329","https://openalex.org/W2036371107","https://openalex.org/W4283264928","https://openalex.org/W2784389591"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"article,":[3],"the":[4,11,24,28,39],"notion":[5],"of":[6,23,38,58,68],"interval-valued":[7,73,76],"preinvex":[8],"functions":[9],"involving":[10],"Riemann\u2013Liouville":[12],"fractional":[13,29,72],"integral":[14,30,69],"is":[15],"described.":[16],"By":[17],"applying":[18],"this,":[19],"some":[20,47],"new":[21],"refinements":[22],"Hermite\u2013Hadamard":[25],"inequality":[26],"for":[27,65,71],"operator":[31],"are":[32,42,49],"presented.":[33],"Some":[34],"novel":[35],"special":[36],"cases":[37],"presented":[40,50],"results":[41],"discussed":[43],"as":[44],"well.":[45],"Also,":[46],"examples":[48],"to":[51],"validate":[52],"our":[53,59],"results.":[54],"The":[55],"established":[56],"outcomes":[57],"article":[60],"may":[61],"open":[62],"another":[63],"direction":[64],"different":[66],"types":[67],"inequalities":[70],"functions,":[74,77],"fuzzy":[75],"and":[78],"their":[79],"associated":[80],"optimization":[81],"problems.":[82]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":17}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}