{"id":"https://openalex.org/W2163860664","doi":"https://doi.org/10.1155/2012/480689","title":"Sharp Bounds by the Generalized Logarithmic Mean for the Geometric Weighted Mean of the Geometric and Harmonic Means","display_name":"Sharp Bounds by the Generalized Logarithmic Mean for the Geometric Weighted Mean of the Geometric and Harmonic Means","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2163860664","doi":"https://doi.org/10.1155/2012/480689","mag":"2163860664"},"language":"en","primary_location":{"id":"doi:10.1155/2012/480689","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/480689","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/480689.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2012/480689.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101678566","display_name":"Wei-Mao Qian","orcid":null},"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":"Wei-Mao Qian","raw_affiliation_strings":["School of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000"],"affiliations":[{"raw_affiliation_string":"School of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000","institution_ids":["https://openalex.org/I3018263800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075157606","display_name":"Bo-Yong Long","orcid":"https://orcid.org/0000-0001-8136-8488"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo-Yong Long","raw_affiliation_strings":["School of Mathematics Science, Anhui University, Hefei 230039"],"affiliations":[{"raw_affiliation_string":"School of Mathematics Science, Anhui University, Hefei 230039","institution_ids":["https://openalex.org/I143868143"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101678566"],"corresponding_institution_ids":["https://openalex.org/I3018263800"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.4143,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.63880422,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2012","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":0.9998999834060669,"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":0.9940999746322632,"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/T11822","display_name":"Analytic and geometric function theory","score":0.993399977684021,"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/harmonic-mean","display_name":"Harmonic mean","score":0.9336960315704346},{"id":"https://openalex.org/keywords/geometric-mean","display_name":"Geometric mean","score":0.9147886037826538},{"id":"https://openalex.org/keywords/logarithmic-mean","display_name":"Logarithmic mean","score":0.9039764404296875},{"id":"https://openalex.org/keywords/weighted-geometric-mean","display_name":"Weighted geometric mean","score":0.8731478452682495},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7938625812530518},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.755299985408783},{"id":"https://openalex.org/keywords/geometric-progression","display_name":"Geometric progression","score":0.5242524147033691},{"id":"https://openalex.org/keywords/generalized-mean","display_name":"Generalized mean","score":0.4624519646167755},{"id":"https://openalex.org/keywords/geometric-shape","display_name":"Geometric shape","score":0.46052107214927673},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.452961266040802},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41180670261383057},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20616811513900757},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09542134404182434}],"concepts":[{"id":"https://openalex.org/C203858083","wikidata":"https://www.wikidata.org/wiki/Q188347","display_name":"Harmonic mean","level":2,"score":0.9336960315704346},{"id":"https://openalex.org/C40222840","wikidata":"https://www.wikidata.org/wiki/Q185049","display_name":"Geometric mean","level":2,"score":0.9147886037826538},{"id":"https://openalex.org/C116119841","wikidata":"https://www.wikidata.org/wiki/Q954389","display_name":"Logarithmic mean","level":3,"score":0.9039764404296875},{"id":"https://openalex.org/C117656884","wikidata":"https://www.wikidata.org/wiki/Q2625569","display_name":"Weighted geometric mean","level":3,"score":0.8731478452682495},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7938625812530518},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.755299985408783},{"id":"https://openalex.org/C14367171","wikidata":"https://www.wikidata.org/wiki/Q173523","display_name":"Geometric progression","level":2,"score":0.5242524147033691},{"id":"https://openalex.org/C117355083","wikidata":"https://www.wikidata.org/wiki/Q855729","display_name":"Generalized mean","level":2,"score":0.4624519646167755},{"id":"https://openalex.org/C7305733","wikidata":"https://www.wikidata.org/wiki/Q207961","display_name":"Geometric shape","level":2,"score":0.46052107214927673},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.452961266040802},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41180670261383057},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20616811513900757},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09542134404182434},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/480689","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/480689","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/480689.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1355495140","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1355495140","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:480689","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/480689.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"pmh:oai:doaj.org/article:12bce071b88f4c1fa4abae8b67dc4bb6","is_oa":true,"landing_page_url":"https://doaj.org/article/12bce071b88f4c1fa4abae8b67dc4bb6","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":"Journal of Applied Mathematics, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/480689","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/480689","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/480689.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2163860664.pdf","grobid_xml":"https://content.openalex.org/works/W2163860664.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W146527998","https://openalex.org/W1550621289","https://openalex.org/W1959975027","https://openalex.org/W1973885318","https://openalex.org/W1986019367","https://openalex.org/W1986951071","https://openalex.org/W2001657156","https://openalex.org/W2020244518","https://openalex.org/W2021343455","https://openalex.org/W2028136887","https://openalex.org/W2033428428","https://openalex.org/W2035875137","https://openalex.org/W2038579603","https://openalex.org/W2039359000","https://openalex.org/W2044218791","https://openalex.org/W2044842791","https://openalex.org/W2062613094","https://openalex.org/W2068058600","https://openalex.org/W2069460390","https://openalex.org/W2069552979","https://openalex.org/W2071112733","https://openalex.org/W2080708534","https://openalex.org/W2088818596","https://openalex.org/W2092797578","https://openalex.org/W2253715404","https://openalex.org/W2260634595","https://openalex.org/W2314192938","https://openalex.org/W2318893458","https://openalex.org/W2319454238","https://openalex.org/W2321571386","https://openalex.org/W2331974025","https://openalex.org/W2562800485","https://openalex.org/W2912469963","https://openalex.org/W4230731707","https://openalex.org/W4235382576","https://openalex.org/W4236700867","https://openalex.org/W4241194388","https://openalex.org/W4248342312","https://openalex.org/W4256015552","https://openalex.org/W4285719527","https://openalex.org/W4385623073"],"related_works":["https://openalex.org/W2002768246","https://openalex.org/W2128177177","https://openalex.org/W4234739562","https://openalex.org/W2096851309","https://openalex.org/W2162063307","https://openalex.org/W4254478543","https://openalex.org/W2150601196","https://openalex.org/W2027369157","https://openalex.org/W2163860664","https://openalex.org/W2808173759"],"abstract_inverted_index":{"We":[0],"present":[1],"sharp":[2],"upper":[3],"and":[4,18],"lower":[5],"generalized":[6],"logarithmic":[7],"mean":[8,14],"bounds":[9],"for":[10],"the":[11,16],"geometric":[12,17],"weighted":[13],"of":[15],"harmonic":[19],"means.":[20]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2016-06-24T00:00:00"}