{"id":"https://openalex.org/W2062484790","doi":"https://doi.org/10.1137/140954015","title":"On a Lower Bound for the Jensen Inequality","display_name":"On a Lower Bound for the Jensen Inequality","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2062484790","doi":"https://doi.org/10.1137/140954015","mag":"2062484790"},"language":"en","primary_location":{"id":"doi:10.1137/140954015","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140954015","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037434634","display_name":"Stephen G. Walker","orcid":"https://orcid.org/0000-0002-0497-238X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Stephen G. Walker","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5037434634"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2808,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.86548085,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"46","issue":"5","first_page":"3151","last_page":"3157"},"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":0.9955000281333923,"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/T12504","display_name":"Mathematics and Applications","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.8909654021263123},{"id":"https://openalex.org/keywords/jensens-inequality","display_name":"Jensen's inequality","score":0.8466525077819824},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.6530214548110962},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5888110995292664},{"id":"https://openalex.org/keywords/kantorovich-inequality","display_name":"Kantorovich inequality","score":0.5848480463027954},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5773047804832458},{"id":"https://openalex.org/keywords/log-sum-inequality","display_name":"Log sum inequality","score":0.5126191973686218},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.49938511848449707},{"id":"https://openalex.org/keywords/h\u00f6lders-inequality","display_name":"H\u00f6lder's inequality","score":0.49767401814460754},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.46247991919517517},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44097819924354553},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.43764862418174744},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4061760902404785},{"id":"https://openalex.org/keywords/linear-inequality","display_name":"Linear inequality","score":0.37247979640960693},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3282204866409302},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.18636560440063477},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.18158769607543945},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07373538613319397}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8909654021263123},{"id":"https://openalex.org/C174169938","wikidata":"https://www.wikidata.org/wiki/Q518131","display_name":"Jensen's inequality","level":5,"score":0.8466525077819824},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.6530214548110962},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5888110995292664},{"id":"https://openalex.org/C206399364","wikidata":"https://www.wikidata.org/wiki/Q3154001","display_name":"Kantorovich inequality","level":4,"score":0.5848480463027954},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5773047804832458},{"id":"https://openalex.org/C46979015","wikidata":"https://www.wikidata.org/wiki/Q6666859","display_name":"Log sum inequality","level":3,"score":0.5126191973686218},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.49938511848449707},{"id":"https://openalex.org/C91558832","wikidata":"https://www.wikidata.org/wiki/Q731894","display_name":"H\u00f6lder's inequality","level":4,"score":0.49767401814460754},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.46247991919517517},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44097819924354553},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43764862418174744},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4061760902404785},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.37247979640960693},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3282204866409302},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.18636560440063477},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.18158769607543945},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07373538613319397},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140954015","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140954015","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6100000143051147,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W2048305092","https://openalex.org/W2051641650","https://openalex.org/W2062551477","https://openalex.org/W2160596340"],"related_works":["https://openalex.org/W2586260151","https://openalex.org/W4319791510","https://openalex.org/W58810707","https://openalex.org/W2378749595","https://openalex.org/W2358303014","https://openalex.org/W2291963200","https://openalex.org/W2039878365","https://openalex.org/W2066353574","https://openalex.org/W584157749","https://openalex.org/W1574966625"],"abstract_inverted_index":{"We":[0],"present":[1],"an":[2,34,46,60],"improvement":[3],"to":[4],"the":[5,23,30,41,54,57],"Jensen":[6,24,31],"inequality":[7,32,43],"for":[8,22,40,64],"certain":[9],"convex":[10],"functions":[11],"$\\phi$":[12,37,50],"on":[13,69],"$(0\\,\\infty)$.":[14],"This":[15],"implies":[16],"finding":[17],"a":[18],"nonzero":[19],"lower":[20],"bound":[21],"gap.":[25],"In":[26],"particular,":[27],"just":[28],"as":[29],"becomes":[33],"equality":[35,47],"when":[36,49],"is":[38,51,59],"linear,":[39],"new":[42,62],"we":[44],"obtain":[45],"also":[48],"quadratic.":[52],"At":[53],"heart":[55],"of":[56],"paper":[58],"apparent":[61],"technique":[63],"improving":[65],"classical":[66],"inequalities":[67],"based":[68],"nonlinear":[70],"functions.":[71]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
