{"id":"https://openalex.org/W3165283026","doi":"https://doi.org/10.3390/sym13060951","title":"New Geometric Constants in Banach Spaces Related to the Inscribed Equilateral Triangles of Unit Balls","display_name":"New Geometric Constants in Banach Spaces Related to the Inscribed Equilateral Triangles of Unit Balls","publication_year":2021,"publication_date":"2021-05-27","ids":{"openalex":"https://openalex.org/W3165283026","doi":"https://doi.org/10.3390/sym13060951","mag":"3165283026"},"language":"en","primary_location":{"id":"doi:10.3390/sym13060951","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13060951","pdf_url":"https://www.mdpi.com/2073-8994/13/6/951/pdf?version=1622105146","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/2073-8994/13/6/951/pdf?version=1622105146","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032701202","display_name":"Yuankang Fu","orcid":"https://orcid.org/0000-0001-8972-1848"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuankang Fu","raw_affiliation_strings":["School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009302809","display_name":"Qi Liu","orcid":"https://orcid.org/0000-0002-6049-5282"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qi Liu","raw_affiliation_strings":["School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China"],"raw_orcid":"https://orcid.org/0000-0002-6049-5282","affiliations":[{"raw_affiliation_string":"School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101561342","display_name":"Yongjin Li","orcid":"https://orcid.org/0000-0003-4322-308X"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yongjin Li","raw_affiliation_strings":["School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China"],"raw_orcid":"https://orcid.org/0000-0003-4322-308X","affiliations":[{"raw_affiliation_string":"School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China","institution_ids":["https://openalex.org/I157773358"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5009302809","https://openalex.org/A5101561342"],"corresponding_institution_ids":["https://openalex.org/I157773358"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.6087,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.71857837,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"13","issue":"6","first_page":"951","last_page":"951"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9945999979972839,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9945999979972839,"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"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9916999936103821,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9905999898910522,"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/inscribed-figure","display_name":"Inscribed figure","score":0.8349336385726929},{"id":"https://openalex.org/keywords/equilateral-triangle","display_name":"Equilateral triangle","score":0.7642822265625},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7204635143280029},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.6478664875030518},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5740424394607544},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.549477219581604},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4718829393386841},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.46424970030784607},{"id":"https://openalex.org/keywords/unit-square","display_name":"Unit square","score":0.45517709851264954},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40106844902038574},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.39566129446029663},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3846335709095001},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3830898702144623},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09072044491767883}],"concepts":[{"id":"https://openalex.org/C44074806","wikidata":"https://www.wikidata.org/wiki/Q1066790","display_name":"Inscribed figure","level":2,"score":0.8349336385726929},{"id":"https://openalex.org/C146786541","wikidata":"https://www.wikidata.org/wiki/Q157002","display_name":"Equilateral triangle","level":2,"score":0.7642822265625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7204635143280029},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6478664875030518},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5740424394607544},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.549477219581604},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4718829393386841},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.46424970030784607},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.45517709851264954},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40106844902038574},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.39566129446029663},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3846335709095001},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3830898702144623},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09072044491767883},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","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":3,"locations":[{"id":"doi:10.3390/sym13060951","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13060951","pdf_url":"https://www.mdpi.com/2073-8994/13/6/951/pdf?version=1622105146","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:bf474475571a4b25b68a696e99faa2ce","is_oa":true,"landing_page_url":"https://doaj.org/article/bf474475571a4b25b68a696e99faa2ce","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"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 13, Iss 6, p 951 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/6/951/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13060951","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/sym13060951","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13060951","pdf_url":"https://www.mdpi.com/2073-8994/13/6/951/pdf?version=1622105146","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/W3165283026.pdf","grobid_xml":"https://content.openalex.org/works/W3165283026.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W610522045","https://openalex.org/W1518096223","https://openalex.org/W1531291633","https://openalex.org/W1555444504","https://openalex.org/W1973789624","https://openalex.org/W1996031842","https://openalex.org/W1996668050","https://openalex.org/W1998411459","https://openalex.org/W2005848700","https://openalex.org/W2007810353","https://openalex.org/W2008181411","https://openalex.org/W2012976574","https://openalex.org/W2018703998","https://openalex.org/W2021136691","https://openalex.org/W2035241147","https://openalex.org/W2060416678","https://openalex.org/W2062187275","https://openalex.org/W2073919430","https://openalex.org/W2078558388","https://openalex.org/W2100316758","https://openalex.org/W2112251421","https://openalex.org/W2140087811","https://openalex.org/W2325276686","https://openalex.org/W2331268210","https://openalex.org/W2498059247","https://openalex.org/W2618678509","https://openalex.org/W4232853762","https://openalex.org/W6633391173","https://openalex.org/W6738852763"],"related_works":["https://openalex.org/W2324974223","https://openalex.org/W3128759501","https://openalex.org/W3102230940","https://openalex.org/W1586759986","https://openalex.org/W4287231084","https://openalex.org/W1570825404","https://openalex.org/W3161375928","https://openalex.org/W222989450","https://openalex.org/W2022929595","https://openalex.org/W2798172748"],"abstract_inverted_index":{"Geometric":[0],"constant":[1],"is":[2],"one":[3],"of":[4,12,40,44,52,61],"the":[5,37,59,92,102],"important":[6],"tools":[7],"to":[8,36],"study":[9],"geometric":[10,23,86],"properties":[11],"Banach":[13,29,71],"spaces.":[14],"In":[15,76],"this":[16],"paper,":[17],"we":[18],"will":[19,73,88,111],"introduce":[20],"two":[21],"new":[22],"constants":[24,87],"JL(X)":[25,53,62],"and":[26,34,49,54,63,68,83,98,101,108],"YJ(X)":[27,55,64,82],"in":[28],"spaces,":[30],"which":[31],"are":[32],"symmetric":[33],"related":[35],"side":[38],"lengths":[39],"inscribed":[41],"equilateral":[42],"triangles":[43],"unit":[45],"balls.":[46],"The":[47],"upper":[48],"lower":[50],"bounds":[51],"as":[56,58],"well":[57],"values":[60],"for":[65,80,95,105],"Hilbert":[66],"spaces":[67,72],"some":[69,78,84],"common":[70],"be":[74,89,112],"calculated.":[75],"addition,":[77],"inequalities":[79],"JL(X),":[81],"significant":[85],"presented.":[90],"Furthermore,":[91],"sufficient":[93],"conditions":[94,104],"uniformly":[96,106,109],"non-square":[97,107],"normal":[99],"structure,":[100],"necessary":[103],"convex":[110],"established.":[113]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
