{"id":"https://openalex.org/W2139154908","doi":null,"title":"Sequence Inequalities for the Logarithmic Convex (Concave) Function","display_name":"Sequence Inequalities for the Logarithmic Convex (Concave) Function","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2139154908","mag":"2139154908"},"language":"en","primary_location":{"id":"pmh:oai:eprints.vu.edu.au:18059","doi":null,"is_oa":false,"landing_page_url":"https://vuir.vu.edu.au/18059/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400215","display_name":"Victoria University Research Repository (Victoria University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I41156924","host_organization_name":"Victoria University of Wellington","host_organization_lineage":["https://openalex.org/I41156924"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5031943931","display_name":"Jian-She Sun","orcid":"https://orcid.org/0000-0001-6373-6427","observed_orcids":["https://orcid.org/0000-0001-6373-6427"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jian-She Sun","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-6373-6427","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5031943931"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3909,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.51006186,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":null,"issue":null,"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":0.9994999766349792,"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":0.9994999766349792,"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.0003000000142492354,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/logarithmic-convexity","display_name":"logarithmic convexity","score":0.828000009059906},{"id":"https://openalex.org/keywords/log-concavity","display_name":"log-concavity","score":0.9990000128746033}],"concepts":[{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.7836617231369019},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7625558376312256},{"id":"https://openalex.org/C66690126","wikidata":"https://www.wikidata.org/wiki/Q2914302","display_name":"Concave function","level":3,"score":0.7499716281890869},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.7339286804199219},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7237388491630554},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6583604216575623},{"id":"https://openalex.org/C136719777","wikidata":"https://www.wikidata.org/wiki/Q3610230","display_name":"Logarithmically convex function","level":5,"score":0.6367736458778381},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5837317705154419},{"id":"https://openalex.org/C56017942","wikidata":"https://www.wikidata.org/wiki/Q204037","display_name":"Natural logarithm","level":3,"score":0.5546947121620178},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5503262877464294},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.540860652923584},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.42765581607818604},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3988698720932007},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.28604090213775635},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23510000109672546},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.18024486303329468},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09131470322608948},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07254549860954285},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:eprints.vu.edu.au:18059","doi":null,"is_oa":false,"landing_page_url":"https://vuir.vu.edu.au/18059/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400215","display_name":"Victoria University Research Repository (Victoria University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I41156924","host_organization_name":"Victoria University of Wellington","host_organization_lineage":["https://openalex.org/I41156924"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"mag:2139154908","doi":null,"is_oa":false,"landing_page_url":"http://ajmaa.org/RGMIA/papers/v7n4/logconv.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1590460147","https://openalex.org/W1997390304","https://openalex.org/W2073242700","https://openalex.org/W2227998922","https://openalex.org/W2468532079","https://openalex.org/W3137092841"],"related_works":["https://openalex.org/W2254794904","https://openalex.org/W2328311852","https://openalex.org/W7057114729","https://openalex.org/W2055060590","https://openalex.org/W2073242700","https://openalex.org/W2123454749","https://openalex.org/W2959833232","https://openalex.org/W7098984702","https://openalex.org/W7125216800","https://openalex.org/W7101041385"],"abstract_inverted_index":{"Let":[0],"f":[1],"be":[2],"a":[3,19,24],"positive":[4],"strictly":[5],"increasing":[6],"logarithmic":[7,10],"convex":[8],"(or":[9],"concave)":[11],"function":[12],"on":[13],"(0;1],":[14],"then,":[15],"for":[16],"k":[17],"being":[18],"nonnegative":[20],"integer":[21],"and":[22],"n":[23],"natural":[25],"number,":[26],"the":[27],"sequence":[28],"1":[29],"P":[30],"n+k":[31],"i=k+1":[32],"lnf(":[33],"i":[34]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T04:12:42.849631","created_date":"2016-06-24T00:00:00"}