{"id":"https://openalex.org/W4226495852","doi":"https://doi.org/10.3390/sym14040717","title":"q1q2-Ostrowski-Type Integral Inequalities Involving Property of Generalized Higher-Order Strongly n-Polynomial Preinvexity","display_name":"q1q2-Ostrowski-Type Integral Inequalities Involving Property of Generalized Higher-Order Strongly n-Polynomial Preinvexity","publication_year":2022,"publication_date":"2022-04-01","ids":{"openalex":"https://openalex.org/W4226495852","doi":"https://doi.org/10.3390/sym14040717"},"language":"en","primary_location":{"id":"doi:10.3390/sym14040717","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14040717","pdf_url":"https://www.mdpi.com/2073-8994/14/4/717/pdf?version=1648803360","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/2073-8994/14/4/717/pdf?version=1648803360","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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":false,"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/A5066464647","display_name":"Miguel Vivas\u2013Cortez","orcid":"https://orcid.org/0000-0002-1567-0264"},"institutions":[{"id":"https://openalex.org/I39398033","display_name":"Pontificia Universidad Cat\u00f3lica del Ecuador","ror":"https://ror.org/02qztda51","country_code":"EC","type":"education","lineage":["https://openalex.org/I39398033"]}],"countries":["EC"],"is_corresponding":true,"raw_author_name":"Miguel Vivas-Cortez","raw_affiliation_strings":["Escuela de Ciencias F\u00edsicas y Matem\u00e1ticas, Facultad de Ciencias Naturales y Exactas, Pontificia Universidad Cat\u00f3lica del Ecuador, Sede Quito 17-01-2184, Ecuador"],"raw_orcid":"https://orcid.org/0000-0002-1567-0264","affiliations":[{"raw_affiliation_string":"Escuela de Ciencias F\u00edsicas y Matem\u00e1ticas, Facultad de Ciencias Naturales y Exactas, Pontificia Universidad Cat\u00f3lica del Ecuador, Sede Quito 17-01-2184, Ecuador","institution_ids":["https://openalex.org/I39398033"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066464647"],"corresponding_institution_ids":["https://openalex.org/I39398033"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.8463,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.90637864,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"14","issue":"4","first_page":"717","last_page":"717"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9814000129699707,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9782000184059143,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.7472274303436279},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.7435815334320068},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5867208242416382},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5825350880622864},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.575538158416748},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5429326295852661},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5110665559768677},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5072600245475769},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4977753460407257},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4756842851638794},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.46653348207473755},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4398791790008545},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3878485858440399},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3848855197429657},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24862006306648254},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07706984877586365}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7472274303436279},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.7435815334320068},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5867208242416382},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5825350880622864},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.575538158416748},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5429326295852661},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5110665559768677},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5072600245475769},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4977753460407257},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4756842851638794},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.46653348207473755},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4398791790008545},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3878485858440399},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3848855197429657},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24862006306648254},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07706984877586365},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14040717","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14040717","pdf_url":"https://www.mdpi.com/2073-8994/14/4/717/pdf?version=1648803360","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:7ebec221f3784e80a51c7ebb7e3273c2","is_oa":true,"landing_page_url":"https://doaj.org/article/7ebec221f3784e80a51c7ebb7e3273c2","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 4, p 717 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/4/717/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14040717","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/sym14040717","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14040717","pdf_url":"https://www.mdpi.com/2073-8994/14/4/717/pdf?version=1648803360","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4226495852.pdf","grobid_xml":"https://content.openalex.org/works/W4226495852.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W566543047","https://openalex.org/W1551245004","https://openalex.org/W1963574764","https://openalex.org/W1993027641","https://openalex.org/W2000983337","https://openalex.org/W2012192004","https://openalex.org/W2026780626","https://openalex.org/W2094786643","https://openalex.org/W2118017323","https://openalex.org/W2322767775","https://openalex.org/W2499795752","https://openalex.org/W2560344843","https://openalex.org/W2953525767","https://openalex.org/W2962387070","https://openalex.org/W2967115160","https://openalex.org/W2997221982","https://openalex.org/W2997932628","https://openalex.org/W2999686232","https://openalex.org/W3006934234","https://openalex.org/W3014434208","https://openalex.org/W3126612424","https://openalex.org/W3134365497","https://openalex.org/W3162607444","https://openalex.org/W3197580818","https://openalex.org/W3214239812","https://openalex.org/W4206381779","https://openalex.org/W4210601435","https://openalex.org/W4240644230","https://openalex.org/W4242820328","https://openalex.org/W6633167009","https://openalex.org/W6640942387"],"related_works":["https://openalex.org/W1996226968","https://openalex.org/W2912909874","https://openalex.org/W4288573727","https://openalex.org/W2494876756","https://openalex.org/W2768754015","https://openalex.org/W2914542058","https://openalex.org/W4398758929","https://openalex.org/W257189624","https://openalex.org/W2393350255","https://openalex.org/W4390176194"],"abstract_inverted_index":{"Quantum":[0,139],"calculus":[1],"has":[2],"numerous":[3],"applications":[4,152],"in":[5,21,39,136,153],"mathematics.":[6],"This":[7,47],"novel":[8],"class":[9,58],"of":[10,19,42,59,83,86,109,133,141,157],"functions":[11,113,118,125],"may":[12],"be":[13],"used":[14,147],"to":[15,52,148],"produce":[16],"a":[17,40,56,73,92,154],"variety":[18,41],"conclusions":[20],"convex":[22],"analysis,":[23],"special":[24],"functions,":[25,61],"quantum":[26],"mechanics,":[27],"related":[28],"optimization":[29],"theory,":[30,89],"and":[31,44,54,97,144],"mathematical":[32],"inequalities.":[33],"It":[34],"can":[35],"drive":[36],"additional":[37],"research":[38],"pure":[43],"applied":[45],"fields.":[46],"article\u2019s":[48],"main":[49],"objective":[50],"is":[51,63,91,161],"introduce":[53],"study":[55],"new":[57,74],"preinvex":[60,69,124],"which":[62],"called":[64],"higher-order":[65,120],"generalized":[66,87,121],"strongly":[67,122],"n-polynomial":[68,123],"function.":[70],"We":[71],"derive":[72,106],"q1q2-integral":[75],"identity":[76],"for":[77,112],"mixed":[78,115],"partial":[79,116],"q1q2-differentiable":[80,117],"functions.":[81],"Because":[82],"the":[84,131,134,145],"nature":[85],"convexity":[88],"there":[90],"strong":[93],"link":[94],"between":[95],"preinvexity":[96],"symmetry.":[98],"Utilizing":[99],"this":[100,142],"as":[101],"an":[102],"auxiliary":[103],"result,":[104],"we":[105],"some":[107],"estimates":[108],"upper":[110],"bound":[111],"whose":[114],"are":[119,130],"on":[126],"co-ordinates.":[127],"Our":[128],"results":[129,135],"generalizations":[132],"earlier":[137],"papers.":[138],"inequalities":[140],"type":[143],"techniques":[146],"solve":[149],"them":[150],"have":[151],"wide":[155],"range":[156],"fields":[158],"where":[159],"symmetry":[160],"important.":[162]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2025-12-10T02:45:41.426853","created_date":"2022-05-05T00:00:00"}