{"id":"https://openalex.org/W3003199273","doi":"https://doi.org/10.3390/sym12020222","title":"New Multi-Parametrized Estimates Having pth-Order Differentiability in Fractional Calculus for Predominating \u210f-Convex Functions in Hilbert Space","display_name":"New Multi-Parametrized Estimates Having pth-Order Differentiability in Fractional Calculus for Predominating \u210f-Convex Functions in Hilbert Space","publication_year":2020,"publication_date":"2020-02-02","ids":{"openalex":"https://openalex.org/W3003199273","doi":"https://doi.org/10.3390/sym12020222","mag":"3003199273"},"language":"en","primary_location":{"id":"doi:10.3390/sym12020222","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12020222","pdf_url":"https://www.mdpi.com/2073-8994/12/2/222/pdf?version=1582904096","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/2073-8994/12/2/222/pdf?version=1582904096","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091446521","display_name":"Saima Rashid","orcid":"https://orcid.org/0000-0001-7137-1720"},"institutions":[{"id":"https://openalex.org/I194348271","display_name":"Government College University, Faisalabad","ror":"https://ror.org/051zgra59","country_code":"PK","type":"education","lineage":["https://openalex.org/I194348271"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Saima Rashid","raw_affiliation_strings":["Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-7137-1720","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan","institution_ids":["https://openalex.org/I194348271"]}]},{"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/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Humaira Kalsoom","raw_affiliation_strings":["School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China"],"raw_orcid":"https://orcid.org/0000-0002-5835-3349","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030968099","display_name":"Zakia Hammouch","orcid":"https://orcid.org/0000-0001-7349-6922"},"institutions":[{"id":"https://openalex.org/I4210153608","display_name":"Universit\u00e9 Moulay Ismail de Meknes","ror":"https://ror.org/04cnscd67","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210153608"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Zakia Hammouch","raw_affiliation_strings":["Faculty of Science and Techniques Moulay Ismail University of Meknes, 52000 Errachidia, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science and Techniques Moulay Ismail University of Meknes, 52000 Errachidia, Morocco","institution_ids":["https://openalex.org/I4210153608"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011331701","display_name":"Rehana Ashraf","orcid":null},"institutions":[{"id":"https://openalex.org/I161237661","display_name":"Lahore College for Women University","ror":"https://ror.org/02bf6br77","country_code":"PK","type":"education","lineage":["https://openalex.org/I161237661"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Rehana Ashraf","raw_affiliation_strings":["Department of Mathematics, Lahore College for Women University, Jhangh Campus, Lahore 54500, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Lahore College for Women University, Jhangh Campus, Lahore 54500, Pakistan","institution_ids":["https://openalex.org/I161237661"]}]},{"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"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Dumitru Baleanu","raw_affiliation_strings":["Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey"],"raw_orcid":"https://orcid.org/0000-0002-0286-7244","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey","institution_ids":["https://openalex.org/I106245021"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046314241","display_name":"Yu\u2010Ming Chu","orcid":"https://orcid.org/0000-0002-0944-2134"},"institutions":[{"id":"https://openalex.org/I3018263800","display_name":"Huzhou University","ror":"https://ror.org/04mvpxy20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3018263800"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yu-Ming Chu","raw_affiliation_strings":["Department of Mathematics, Huzhou University, Huzhou 313000, China"],"raw_orcid":"https://orcid.org/0000-0002-0944-2134","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Huzhou University, Huzhou 313000, China","institution_ids":["https://openalex.org/I3018263800"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5046314241"],"corresponding_institution_ids":["https://openalex.org/I3018263800"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":12.2795,"has_fulltext":true,"cited_by_count":46,"citation_normalized_percentile":{"value":0.99339181,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"12","issue":"2","first_page":"222","last_page":"222"},"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/T12508","display_name":"Functional Equations Stability Results","score":0.9678999781608582,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9602000117301941,"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/quasiconvex-function","display_name":"Quasiconvex function","score":0.8387030959129333},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6868904232978821},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6274983286857605},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5742000937461853},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5670225620269775},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.5411443710327148},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.49045202136039734},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.48371413350105286},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.4601159691810608},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4514656066894531},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.4436352550983429},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4368543028831482},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.41902562975883484},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.4183715283870697},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.406107097864151},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34027794003486633},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.23718923330307007}],"concepts":[{"id":"https://openalex.org/C80278974","wikidata":"https://www.wikidata.org/wiki/Q1126412","display_name":"Quasiconvex function","level":5,"score":0.8387030959129333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6868904232978821},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6274983286857605},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5742000937461853},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5670225620269775},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.5411443710327148},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.49045202136039734},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.48371413350105286},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.4601159691810608},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4514656066894531},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.4436352550983429},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4368543028831482},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.41902562975883484},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.4183715283870697},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.406107097864151},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34027794003486633},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.23718923330307007},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"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/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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12020222","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12020222","pdf_url":"https://www.mdpi.com/2073-8994/12/2/222/pdf?version=1582904096","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:0a644d5e6bfe4dff9581f1bc1ac2ef18","is_oa":true,"landing_page_url":"https://doaj.org/article/0a644d5e6bfe4dff9581f1bc1ac2ef18","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 2, p 222 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/2/222/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym12020222","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/sym12020222","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12020222","pdf_url":"https://www.mdpi.com/2073-8994/12/2/222/pdf?version=1582904096","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":[{"id":"https://openalex.org/G1064001500","display_name":null,"funder_award_id":"61673169","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1217450499","display_name":null,"funder_award_id":"2018YZ07","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1668911281","display_name":null,"funder_award_id":"61673169, 11301127, 11701176, 11626101, 11601485","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G171498429","display_name":null,"funder_award_id":"11601485","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4483441822","display_name":null,"funder_award_id":"61673169, 11301127, 11701176","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4499578435","display_name":null,"funder_award_id":"11701176, 11626101, 11601485","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4844902455","display_name":null,"funder_award_id":"11626101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4858060408","display_name":null,"funder_award_id":"11701176","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5376261061","display_name":null,"funder_award_id":"11301127","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3003199273.pdf","grobid_xml":"https://content.openalex.org/works/W3003199273.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W47555992","https://openalex.org/W315148139","https://openalex.org/W433794350","https://openalex.org/W1536614419","https://openalex.org/W1553338987","https://openalex.org/W1972478479","https://openalex.org/W1984379533","https://openalex.org/W1984853762","https://openalex.org/W1999083556","https://openalex.org/W2006458314","https://openalex.org/W2019761544","https://openalex.org/W2026160650","https://openalex.org/W2028175209","https://openalex.org/W2049888876","https://openalex.org/W2067080690","https://openalex.org/W2071593170","https://openalex.org/W2082858262","https://openalex.org/W2322995112","https://openalex.org/W2428950989","https://openalex.org/W2488882192","https://openalex.org/W2508689004","https://openalex.org/W2787696370","https://openalex.org/W2787959293","https://openalex.org/W2788828518","https://openalex.org/W2789265722","https://openalex.org/W2795777465","https://openalex.org/W2899874324","https://openalex.org/W2909610461","https://openalex.org/W2909768556","https://openalex.org/W2912759054","https://openalex.org/W2916728564","https://openalex.org/W2936177167","https://openalex.org/W2943232059","https://openalex.org/W2943461950","https://openalex.org/W2955207539","https://openalex.org/W2967854400","https://openalex.org/W2970687766","https://openalex.org/W2987132035","https://openalex.org/W2990568942","https://openalex.org/W2997932628","https://openalex.org/W3099870866","https://openalex.org/W6722480987","https://openalex.org/W6748084325","https://openalex.org/W6748902012","https://openalex.org/W6758079898","https://openalex.org/W6758516612","https://openalex.org/W6762144023"],"related_works":["https://openalex.org/W2101504640","https://openalex.org/W2007576447","https://openalex.org/W2026600343","https://openalex.org/W2356261519","https://openalex.org/W2053616442","https://openalex.org/W4382519084","https://openalex.org/W2478309485","https://openalex.org/W4361807553","https://openalex.org/W165488893","https://openalex.org/W2485727134"],"abstract_inverted_index":{"In":[0],"Hilbert":[1],"space,":[2],"we":[3],"develop":[4],"a":[5,25,80,132],"novel":[6,100],"framework":[7],"to":[8,35,98,103],"study":[9,119],"for":[10,107,124],"two":[11],"new":[12,122],"classes":[13,59,62],"of":[14,44,51,63,73,79,93,131],"convex":[15],"function":[16,28],"depending":[17],"on":[18],"arbitrary":[19],"non-negative":[20],"function,":[21,32],"which":[22],"is":[23,55,88,114],"called":[24],"predominating":[26,30],"\u210f-convex":[27,71],"and":[29,47,75],"quasiconvex":[31,77],"with":[33,48],"respect":[34],"\u03b7":[36,64,67],",":[37],"are":[38],"presented.":[39],"To":[40],"ensure":[41],"the":[42,49,91,104],"symmetry":[43],"data":[45],"segmentation":[46],"discussion":[50],"special":[52],"cases,":[53],"it":[54],"shown":[56],"that":[57,116],"these":[58],"capture":[60],"other":[61],"-convex":[65],"functions,":[66,69],"-quasiconvex":[68],"strongly":[70,76],"functions":[72,78],"higher-order":[74],"higher":[81],"order,":[82],"etc.":[83],"Meanwhile,":[84],"an":[85],"auxiliary":[86],"result":[87],"proved":[89],"in":[90,127],"sense":[92],"\u03ba":[94],"-fractional":[95],"integral":[96],"operator":[97],"generate":[99],"variants":[101],"related":[102],"Hermite\u2013Hadamard":[105],"type":[106],"p":[108],"t":[109],"h":[110],"-order":[111],"differentiability.":[112],"It":[113],"hoped":[115],"this":[117],"research":[118],"will":[120],"open":[121],"doors":[123],"in-depth":[125],"investigation":[126],"convexity":[128],"theory":[129],"frameworks":[130],"varying":[133],"nature.":[134]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":13}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2020-02-07T00:00:00"}