{"id":"https://openalex.org/W3014323014","doi":"https://doi.org/10.1080/00029890.2020.1704168","title":"A Short Proof that Some Mappings of the Unit Ball of <i>\u2113</i><sub>2</sub> Are Never Nonexpansive","display_name":"A Short Proof that Some Mappings of the Unit Ball of <i>\u2113</i><sub>2</sub> Are Never Nonexpansive","publication_year":2020,"publication_date":"2020-03-30","ids":{"openalex":"https://openalex.org/W3014323014","doi":"https://doi.org/10.1080/00029890.2020.1704168","mag":"3014323014"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2020.1704168","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1704168","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","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/A5102099851","display_name":"Jes\u00fas Ferrer","orcid":null},"institutions":[{"id":"https://openalex.org/I16097986","display_name":"Universitat de Val\u00e8ncia","ror":"https://ror.org/043nxc105","country_code":"ES","type":"education","lineage":["https://openalex.org/I16097986"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Jes\u00fas Ferrer","raw_affiliation_strings":["Departamento de An\u00e0lisis Matem\u00e0tico, Universidad de Val\u00e8ncia, Dr. Moliner, 50, 46100 Burjassot (Val\u00e8ncia), Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de An\u00e0lisis Matem\u00e0tico, Universidad de Val\u00e8ncia, Dr. Moliner, 50, 46100 Burjassot (Val\u00e8ncia), Spain","institution_ids":["https://openalex.org/I16097986"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044714032","display_name":"Enrique Llorens-Fuster","orcid":"https://orcid.org/0000-0001-6194-0002"},"institutions":[{"id":"https://openalex.org/I16097986","display_name":"Universitat de Val\u00e8ncia","ror":"https://ror.org/043nxc105","country_code":"ES","type":"education","lineage":["https://openalex.org/I16097986"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Enrique Llorens-Fuster","raw_affiliation_strings":["Departamento de An\u00e0lisis Matem\u00e0tico, Universidad de Val\u00e8ncia, Dr. Moliner, 50, 46100 Burjassot (Val\u00e8ncia), Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de An\u00e0lisis Matem\u00e0tico, Universidad de Val\u00e8ncia, Dr. Moliner, 50, 46100 Burjassot (Val\u00e8ncia), Spain","institution_ids":["https://openalex.org/I16097986"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102099851"],"corresponding_institution_ids":["https://openalex.org/I16097986"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11556671,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"127","issue":"4","first_page":"354","last_page":"358"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9986000061035156,"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":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.7836665511131287},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.756977915763855},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6734589338302612},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6124588251113892},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.49681714177131653},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.4700514078140259},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40334075689315796},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39108431339263916},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34715574979782104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24695590138435364},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11241310834884644},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.04683646559715271}],"concepts":[{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.7836665511131287},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.756977915763855},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6734589338302612},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6124588251113892},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.49681714177131653},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.4700514078140259},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40334075689315796},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39108431339263916},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34715574979782104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24695590138435364},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11241310834884644},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.04683646559715271},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2020.1704168","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1704168","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W177016572","https://openalex.org/W1489200767","https://openalex.org/W1640559147","https://openalex.org/W1970771702","https://openalex.org/W1973395374","https://openalex.org/W2008181411","https://openalex.org/W2026851807","https://openalex.org/W2311011274","https://openalex.org/W2313944420","https://openalex.org/W2314943822","https://openalex.org/W2327789793","https://openalex.org/W2801847334","https://openalex.org/W4247757876"],"related_works":["https://openalex.org/W2387072865","https://openalex.org/W2804455714","https://openalex.org/W2048403683","https://openalex.org/W3046438935","https://openalex.org/W2989846825","https://openalex.org/W2013083117","https://openalex.org/W2388183907","https://openalex.org/W4231727339","https://openalex.org/W2314727157","https://openalex.org/W2964574560"],"abstract_inverted_index":{"It":[0],"is":[1],"known":[2],"that":[3,45],"some":[4],"particular":[5],"self-mappings":[6],"of":[7,13,27,35,43],"the":[8],"closed":[9,40],"unit":[10],"ball":[11],"B\u21132":[12,44],"\u21132":[14],"with":[15,22],"no":[16],"fixed":[17],"points":[18],"cannot":[19],"be":[20],"nonexpansive":[21],"respect":[23],"to":[24],"any":[25,39],"renorming":[26],"\u21132.":[28],"We":[29],"give":[30],"here":[31],"a":[32],"short":[33],"proof":[34],"this":[36],"fact":[37],"for":[38],"convex":[41],"subset":[42],"these":[46],"mappings":[47],"leave":[48],"invariant.":[49]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}