{"id":"https://openalex.org/W1977348583","doi":"https://doi.org/10.1090/s0002-9939-1962-0143006-9","title":"On the Simultaneous Solution of a Certain System of Linear Inequalities","display_name":"On the Simultaneous Solution of a Certain System of Linear Inequalities","publication_year":1962,"publication_date":"1962-01-01","ids":{"openalex":"https://openalex.org/W1977348583","doi":"https://doi.org/10.1090/s0002-9939-1962-0143006-9","mag":"1977348583"},"language":"en","primary_location":{"id":"doi:10.1090/s0002-9939-1962-0143006-9","doi":"https://doi.org/10.1090/s0002-9939-1962-0143006-9","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0002-9939-1962-0143006-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210226894","display_name":"Proceedings of the American Mathematical Society","issn_l":"0002-9939","issn":["0002-9939","1088-6826"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the American Mathematical Society","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/proc/1962-013-01/S0002-9939-1962-0143006-9/S0002-9939-1962-0143006-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088620397","display_name":"George J. Minty","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"George J. Minty","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5088620397"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9423,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.76551724,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"13","issue":"1","first_page":"11","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.45680001378059387,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11545","display_name":"Advanced Banach Space Theory","score":0.45680001378059387,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.17589999735355377,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.054999999701976776,"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/hilbert-spaces","display_name":"Hilbert spaces","score":0.7799999713897705},{"id":"https://openalex.org/keywords/existence-of-solutions","display_name":"existence of solutions","score":0.41999998688697815}],"concepts":[{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.6442216038703918},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6289608478546143},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6066654920578003},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5254746675491333},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4333984851837158},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4295976161956787},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34639036655426025},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21522396802902222},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08188280463218689},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0002-9939-1962-0143006-9","doi":"https://doi.org/10.1090/s0002-9939-1962-0143006-9","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0002-9939-1962-0143006-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210226894","display_name":"Proceedings of the American Mathematical Society","issn_l":"0002-9939","issn":["0002-9939","1088-6826"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the American Mathematical Society","raw_type":"journal-article"},{"id":"doi:10.2307/2033762","doi":"https://doi.org/10.2307/2033762","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2033762","pdf_url":"https://www.ams.org/proc/1962-013-01/S0002-9939-1962-0143006-9/S0002-9939-1962-0143006-9.pdf","source":{"id":"https://openalex.org/S4210226894","display_name":"Proceedings of the American Mathematical Society","issn_l":"0002-9939","issn":["0002-9939","1088-6826"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the American Mathematical Society","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.2307/2033762","doi":"https://doi.org/10.2307/2033762","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2033762","pdf_url":"https://www.ams.org/proc/1962-013-01/S0002-9939-1962-0143006-9/S0002-9939-1962-0143006-9.pdf","source":{"id":"https://openalex.org/S4210226894","display_name":"Proceedings of the American Mathematical Society","issn_l":"0002-9939","issn":["0002-9939","1088-6826"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the American Mathematical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1977348583.pdf","grobid_xml":"https://content.openalex.org/works/W1977348583.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2091311522","https://openalex.org/W2315731753","https://openalex.org/W2331236532","https://openalex.org/W4234144661","https://openalex.org/W4237936674","https://openalex.org/W4311630515"],"related_works":["https://openalex.org/W2047892901","https://openalex.org/W2007325497","https://openalex.org/W2010308536","https://openalex.org/W2980212679","https://openalex.org/W2063096868","https://openalex.org/W1972375392","https://openalex.org/W1997066917","https://openalex.org/W1972554774","https://openalex.org/W1999054827","https://openalex.org/W2051307219"],"abstract_inverted_index":{"The":[0,73],"author":[1],"recently":[2],"proved":[3],"the":[4,130,186,197,248],"following":[5],"theorem:":[6],"THEOREM":[7],"1.":[8,115,243],"Let":[9,25,125,183],"X":[10],"be":[11,34,53,127,147,185,196,247],"a":[12,61,95,110,162,228],"Hilbert":[13],"space,":[14],"with":[15,129],"real":[16],"or":[17],"complex":[18],"scalars":[19,133],"and":[20,30,50,90,101,104,134,137,193,240],"inner":[21,135],"product":[22],"(x,":[23],"y).":[24],"xi,":[26,40,139,192],"*":[27,32,143,144,176],"*,":[28],"xa":[29],"yi,":[31,142],"ym":[33,146],"given":[35,148],"such":[36,64,149,165,233],"that":[37,65,150,166,234],"(1)":[38],"Re(x":[39],"y":[41,63,164],"yi)":[42,172],"2!":[43],"0":[44,156,232,239],"(;i,":[45],"=":[46,174,238,242,264],"1,":[47,175],"...":[48],")":[49,72],"let":[51,138,194],"x":[52],"any":[54],"point":[55,62,163],"of":[56,81,113],"X.":[57],"Then":[58,159,205,250],"there":[59,160,213,226],"exists":[60,161,227],"(2)":[66],"Re(xi":[67],"-x,":[68],"yiy)":[69],"_":[70,155],"0i=1":[71],"proof":[74,80,112],"was":[75],"patterned":[76],"after":[77],"Schoenberg's":[78,91],"[3]":[79],"Kirszbraun's":[82,102],"theorem.":[83],"B.":[84],"Griinbaum":[85],"[2]":[86],"has":[87,108],"generalized":[88],"my":[89],"proofs":[92],"to":[93,209,246],"obtain":[94],"theorem":[96],"which":[97],"incorporates":[98],"Theorem":[99,114,222,224],"1":[100],"theorem,":[103],"J.":[105],"G.":[106],"Wendel":[107],"contributed":[109],"neater":[111],"With":[116],"Professor":[117],"Wendel's":[118],"permission,":[119],"I":[120],"reproduce":[121],"his":[122],"proof:":[123],"LEMMA.":[124,182],"XE":[126],"En,":[128],"usual":[131],"(real)":[132],"product,":[136],",":[140,145,177],"x..;":[141],"(11)":[151],"(Xi":[152],"Xj)":[153],"y-yj)":[154],"(i=":[157],"*Xm)":[158],"(2')":[167,206],"(x;,":[168],"y)":[169],"<":[170,231],"(xi,":[171,203],"(i":[173],"m).":[178],"PROOF":[179],"OF":[180],"THE":[181],"A":[184],"matrix":[187],"whose":[188,199],"ith":[189,200],"row":[190],"is":[191,202,207,214],"b":[195],"column-vector":[198],"element":[201],"yi).":[204],"equivalent":[208],"Ay_":[210],"b.":[211],"If":[212],"no":[215],"solution":[216],"for":[217,257],"y,":[218],"then":[219],"by":[220],"Stiemke's":[221],"[1,":[223],"2.7]":[225],"row-vector":[229],"n":[230],"(3a,":[235],"3b)":[236],"qA":[237],"qb":[241],"Suppose":[244],"this":[245],"case.":[249],"(3a)":[251],"implies":[252],"Ei":[253],"nixi=":[254],"0,":[255],"hence":[256],"each":[258],"j,":[259],"(4)":[260],"E":[261],"ni(xi,":[262],"yj)":[263],"0.":[265]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
