{"id":"https://openalex.org/W2295691102","doi":"https://doi.org/10.1007/978-3-319-18161-5_36","title":"The Nonlinear Separation Theorem and a Representation Theorem for Bishop\u2013Phelps Cones","display_name":"The Nonlinear Separation Theorem and a Representation Theorem for Bishop\u2013Phelps Cones","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2295691102","doi":"https://doi.org/10.1007/978-3-319-18161-5_36","mag":"2295691102"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-18161-5_36","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-18161-5_36","pdf_url":null,"source":{"id":"https://openalex.org/S2764905038","display_name":"Advances in intelligent systems and computing","issn_l":"2194-5357","issn":["2194-5357","2194-5365"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Intelligent Systems and Computing","raw_type":"book-chapter"},"type":"book-chapter","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/A5061606912","display_name":"Refail Kas\u0131mbeyli","orcid":"https://orcid.org/0000-0002-7339-9409"},"institutions":[{"id":"https://openalex.org/I4210091745","display_name":"Eski\u015fehir City Hospital","ror":"https://ror.org/00czdkn85","country_code":"TR","type":"healthcare","lineage":["https://openalex.org/I1303077703","https://openalex.org/I4210091745"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Refail Kasimbeyli","raw_affiliation_strings":["Faculty of Engineering, Department of Industrial Engineering, Aandolu University, Iki Eylul Campus, Eskisehir, 26555, Turkey"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Department of Industrial Engineering, Aandolu University, Iki Eylul Campus, Eskisehir, 26555, Turkey","institution_ids":["https://openalex.org/I4210091745"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082869161","display_name":"Nergiz Kas\u0131mbeyli","orcid":null},"institutions":[{"id":"https://openalex.org/I4210091745","display_name":"Eski\u015fehir City Hospital","ror":"https://ror.org/00czdkn85","country_code":"TR","type":"healthcare","lineage":["https://openalex.org/I1303077703","https://openalex.org/I4210091745"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Nergiz Kasimbeyli","raw_affiliation_strings":["Faculty of Engineering, Department of Industrial Engineering, Aandolu University, Iki Eylul Campus, Eskisehir, 26555, Turkey"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Department of Industrial Engineering, Aandolu University, Iki Eylul Campus, Eskisehir, 26555, Turkey","institution_ids":["https://openalex.org/I4210091745"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061606912"],"corresponding_institution_ids":["https://openalex.org/I4210091745"],"apc_list":null,"apc_paid":null,"fwci":0.4627,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.66016837,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"419","last_page":"430"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9994000196456909,"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":0.9994000196456909,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9800000190734863,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8177891969680786},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.8113903999328613},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7119035124778748},{"id":"https://openalex.org/keywords/representation-theorem","display_name":"Representation theorem","score":0.705713152885437},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5582679510116577},{"id":"https://openalex.org/keywords/open-mapping-theorem","display_name":"Open mapping theorem (functional analysis)","score":0.5407995581626892},{"id":"https://openalex.org/keywords/brouwer-fixed-point-theorem","display_name":"Brouwer fixed-point theorem","score":0.5230761170387268},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4757263958454132},{"id":"https://openalex.org/keywords/mutual-fund-separation-theorem","display_name":"Mutual fund separation theorem","score":0.45312950015068054},{"id":"https://openalex.org/keywords/picard\u2013lindel\u00f6f-theorem","display_name":"Picard\u2013Lindel\u00f6f theorem","score":0.4479055106639862},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4277181327342987},{"id":"https://openalex.org/keywords/eberlein\u2013\u0161mulian-theorem","display_name":"Eberlein\u2013\u0160mulian theorem","score":0.4252047538757324},{"id":"https://openalex.org/keywords/kelvin\u2013stokes-theorem","display_name":"Kelvin\u2013Stokes theorem","score":0.42125025391578674},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4209296405315399},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4040871262550354},{"id":"https://openalex.org/keywords/danskins-theorem","display_name":"Danskin's theorem","score":0.3689624071121216},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.2610129117965698},{"id":"https://openalex.org/keywords/lp-space","display_name":"Lp space","score":0.07427400350570679},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.05688577890396118},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.053600579500198364},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.04696020483970642}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8177891969680786},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.8113903999328613},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7119035124778748},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.705713152885437},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5582679510116577},{"id":"https://openalex.org/C42030387","wikidata":"https://www.wikidata.org/wiki/Q944297","display_name":"Open mapping theorem (functional analysis)","level":5,"score":0.5407995581626892},{"id":"https://openalex.org/C146147875","wikidata":"https://www.wikidata.org/wiki/Q1144897","display_name":"Brouwer fixed-point theorem","level":3,"score":0.5230761170387268},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4757263958454132},{"id":"https://openalex.org/C160471959","wikidata":"https://www.wikidata.org/wiki/Q17082552","display_name":"Mutual fund separation theorem","level":3,"score":0.45312950015068054},{"id":"https://openalex.org/C206929604","wikidata":"https://www.wikidata.org/wiki/Q530152","display_name":"Picard\u2013Lindel\u00f6f theorem","level":3,"score":0.4479055106639862},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4277181327342987},{"id":"https://openalex.org/C184908153","wikidata":"https://www.wikidata.org/wiki/Q2226650","display_name":"Eberlein\u2013\u0160mulian theorem","level":4,"score":0.4252047538757324},{"id":"https://openalex.org/C198470675","wikidata":"https://www.wikidata.org/wiki/Q3983971","display_name":"Kelvin\u2013Stokes theorem","level":5,"score":0.42125025391578674},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4209296405315399},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4040871262550354},{"id":"https://openalex.org/C48540410","wikidata":"https://www.wikidata.org/wiki/Q5221089","display_name":"Danskin's theorem","level":4,"score":0.3689624071121216},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.2610129117965698},{"id":"https://openalex.org/C172294467","wikidata":"https://www.wikidata.org/wiki/Q305936","display_name":"Lp space","level":3,"score":0.07427400350570679},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.05688577890396118},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.053600579500198364},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.04696020483970642},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-319-18161-5_36","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-18161-5_36","pdf_url":null,"source":{"id":"https://openalex.org/S2764905038","display_name":"Advances in intelligent systems and computing","issn_l":"2194-5357","issn":["2194-5357","2194-5365"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Intelligent Systems and Computing","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6100000143051147}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W189442850","https://openalex.org/W1981808152","https://openalex.org/W1995545738","https://openalex.org/W1998684195","https://openalex.org/W2019916284","https://openalex.org/W2033063724","https://openalex.org/W2037162925","https://openalex.org/W2046254531","https://openalex.org/W2050510066","https://openalex.org/W2091216292","https://openalex.org/W2235662472","https://openalex.org/W2515170017"],"related_works":["https://openalex.org/W3147481289","https://openalex.org/W2769621439","https://openalex.org/W1486807441","https://openalex.org/W1977021713","https://openalex.org/W2821365719","https://openalex.org/W2263301667","https://openalex.org/W2295691102","https://openalex.org/W4237367774","https://openalex.org/W2064345577","https://openalex.org/W2106365219"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}