{"id":"https://openalex.org/W2562812463","doi":"https://doi.org/10.1137/15m1054997","title":"Some Generalizations of the Weierstrass Theorem","display_name":"Some Generalizations of the Weierstrass Theorem","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2562812463","doi":"https://doi.org/10.1137/15m1054997","mag":"2562812463"},"language":"en","primary_location":{"id":"doi:10.1137/15m1054997","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1054997","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","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/A5056555571","display_name":"A. Amini-Harandi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"A. Amini-Harandi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012651854","display_name":"M. Fakhar","orcid":"https://orcid.org/0000-0003-4488-5819"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Fakhar","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078086388","display_name":"H. R. Hajisharifi","orcid":"https://orcid.org/0000-0002-7438-8074"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H. R. Hajisharifi","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5056555571"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3485,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.69359409,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"26","issue":"4","first_page":"2847","last_page":"2862"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9976000189781189,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9976000189781189,"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":0.8946360349655151},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.8203179836273193},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7300934791564941},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.6490993499755859},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5194265842437744},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4327506124973297},{"id":"https://openalex.org/keywords/function-space","display_name":"Function space","score":0.4322684109210968},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4278588891029358},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3727589249610901},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31686535477638245}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8946360349655151},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8203179836273193},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7300934791564941},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6490993499755859},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5194265842437744},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4327506124973297},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.4322684109210968},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4278588891029358},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3727589249610901},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31686535477638245},{"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1054997","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1054997","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3555194478","display_name":null,"funder_award_id":"94470412","funder_id":"https://openalex.org/F4320323645","funder_display_name":"Institute for Research in Fundamental Sciences"},{"id":"https://openalex.org/G5328453752","display_name":null,"funder_award_id":"93550414","funder_id":"https://openalex.org/F4320323645","funder_display_name":"Institute for Research in Fundamental Sciences"}],"funders":[{"id":"https://openalex.org/F4320323645","display_name":"Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1986633045","https://openalex.org/W2006542997","https://openalex.org/W2009708701","https://openalex.org/W2028758638","https://openalex.org/W2042885811","https://openalex.org/W2043907399","https://openalex.org/W2048213039","https://openalex.org/W2051660950","https://openalex.org/W2063676316","https://openalex.org/W2066551529","https://openalex.org/W2072615656","https://openalex.org/W2083872290","https://openalex.org/W2084328130","https://openalex.org/W2086510812"],"related_works":["https://openalex.org/W2073830770","https://openalex.org/W1986685357","https://openalex.org/W2372937593","https://openalex.org/W1976002985","https://openalex.org/W2032699213","https://openalex.org/W206731196","https://openalex.org/W2394377613","https://openalex.org/W2357519649","https://openalex.org/W646185920","https://openalex.org/W132586823"],"abstract_inverted_index":{"The":[0],"main":[1],"goal":[2],"of":[3,11,31,59,75,81,85,101,104,110,122],"this":[4,27],"paper":[5],"is":[6,40,54,69],"to":[7],"obtain":[8],"a":[9,32,37,48,105,108,116],"generalization":[10,109],"the":[12,29,57,60,73,79,99,111,119],"Weierstrass":[13],"theorem":[14,50],"for":[15,51,63],"transfer":[16,89],"weakly":[17,90],"lower":[18,91],"continuous":[19,92],"functions":[20,53,68,93],"on":[21,36,118],"noncompact":[22],"topological":[23,38],"spaces.":[24],"To":[25],"achieve":[26],"goal,":[28],"notion":[30],"quasi-regular-global-inf":[33],"(qrgi)":[34],"function":[35],"space":[39],"introduced,":[41],"some":[42],"equivalent":[43],"statements":[44],"are":[45,94],"given,":[46],"and":[47,66,88,114],"Weierstrass-type":[49],"such":[52],"proved.":[55],"Moreover,":[56],"well-posedness":[58],"minimization":[61,120],"problem":[62,121],"regular-global-inf":[64],"(rgi)":[65],"qrgi":[67,87],"studied.":[70],"Furthermore,":[71],"in":[72],"setting":[74],"reflexive":[76],"Banach":[77],"spaces":[78],"existence":[80],"global":[82],"minimum":[83],"points":[84],"noncoercive":[86],"investigated.":[95],"We":[96],"also":[97],"introduce":[98],"concept":[100],"nearly":[102],"quasi-convexity":[103,112],"function,":[106],"as":[107],"notion,":[113],"present":[115],"result":[117],"these":[123],"functions.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}