{"id":"https://openalex.org/W1964224373","doi":"https://doi.org/10.1007/s10898-013-0051-4","title":"Strongly convex set-valued maps","display_name":"Strongly convex set-valued maps","publication_year":2013,"publication_date":"2013-03-11","ids":{"openalex":"https://openalex.org/W1964224373","doi":"https://doi.org/10.1007/s10898-013-0051-4","mag":"1964224373"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-013-0051-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-013-0051-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-013-0051-4.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10898-013-0051-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102919368","display_name":"Hugo Leiva","orcid":"https://orcid.org/0000-0002-9542-840X"},"institutions":[{"id":"https://openalex.org/I203303854","display_name":"University of the Andes","ror":"https://ror.org/02h1b1x27","country_code":"VE","type":"education","lineage":["https://openalex.org/I203303854"]},{"id":"https://openalex.org/I4210143738","display_name":"Universidad de Los Andes","ror":"https://ror.org/04pqpvr75","country_code":"BO","type":"education","lineage":["https://openalex.org/I4210143738"]}],"countries":["BO","VE"],"is_corresponding":true,"raw_author_name":"Hugo Leiva","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Facultad de Ciencias, Universidad de los Andes, M\u00e9rida, Venezuela","Universidad de los Andes;"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Facultad de Ciencias, Universidad de los Andes, M\u00e9rida, Venezuela","institution_ids":["https://openalex.org/I203303854"]},{"raw_affiliation_string":"Universidad de los Andes;","institution_ids":["https://openalex.org/I4210143738"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112259942","display_name":"Nelson Merentes","orcid":null},"institutions":[{"id":"https://openalex.org/I82002896","display_name":"Central University of Venezuela","ror":"https://ror.org/05kacnm89","country_code":"VE","type":"education","lineage":["https://openalex.org/I82002896"]}],"countries":["VE"],"is_corresponding":false,"raw_author_name":"Nelson Merentes","raw_affiliation_strings":["Escuela de Matem\u00e1ticas, Universidad Central de Venezuela, Caracas, Venezuela","Universidad Central de Venezuela"],"affiliations":[{"raw_affiliation_string":"Escuela de Matem\u00e1ticas, Universidad Central de Venezuela, Caracas, Venezuela","institution_ids":["https://openalex.org/I82002896"]},{"raw_affiliation_string":"Universidad Central de Venezuela","institution_ids":["https://openalex.org/I82002896"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048787304","display_name":"Kazimierz Nikodem","orcid":"https://orcid.org/0000-0001-9458-2272"},"institutions":[{"id":"https://openalex.org/I62088572","display_name":"University of Bielsko-Bia\u0142a","ror":"https://ror.org/01ew38b77","country_code":"PL","type":"education","lineage":["https://openalex.org/I62088572"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Kazimierz Nikodem","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Bielsko-Bia\u0142a, ul. Willowa 2, 43-309 , Bielsko-Bia\u0142a, Poland","University of Bielsko \u2013 Bia\u0142a"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Bielsko-Bia\u0142a, ul. Willowa 2, 43-309 , Bielsko-Bia\u0142a, Poland","institution_ids":["https://openalex.org/I62088572"]},{"raw_affiliation_string":"University of Bielsko \u2013 Bia\u0142a","institution_ids":["https://openalex.org/I62088572"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100631801","display_name":"Jos\u00e9 L. S\u00e1nchez","orcid":"https://orcid.org/0000-0002-8128-3457"},"institutions":[{"id":"https://openalex.org/I82002896","display_name":"Central University of Venezuela","ror":"https://ror.org/05kacnm89","country_code":"VE","type":"education","lineage":["https://openalex.org/I82002896"]}],"countries":["VE"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 Luis S\u00e1nchez","raw_affiliation_strings":["Escuela de Matem\u00e1ticas, Universidad Central de Venezuela, Caracas, Venezuela","Universidad Central de Venezuela"],"affiliations":[{"raw_affiliation_string":"Escuela de Matem\u00e1ticas, Universidad Central de Venezuela, Caracas, Venezuela","institution_ids":["https://openalex.org/I82002896"]},{"raw_affiliation_string":"Universidad Central de Venezuela","institution_ids":["https://openalex.org/I82002896"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5102919368"],"corresponding_institution_ids":["https://openalex.org/I203303854","https://openalex.org/I4210143738"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2780},"fwci":1.8493,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.84611491,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"57","issue":"3","first_page":"695","last_page":"705"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9993000030517578,"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":0.9993000030517578,"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/T12508","display_name":"Functional Equations Stability Results","score":0.9970999956130981,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.984499990940094,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.8839799165725708},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.7219312191009521},{"id":"https://openalex.org/keywords/absolutely-convex-set","display_name":"Absolutely convex set","score":0.7039151191711426},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.643337607383728},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.5777524709701538},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5198310017585754},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5182871222496033},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.5123502016067505},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47380298376083374},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.46505364775657654},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4530446529388428},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.44221609830856323},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.4337017834186554},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.42716753482818604},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41874659061431885},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.41302046179771423},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.366491436958313},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.25739872455596924},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10477778315544128},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.053319185972213745}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8839799165725708},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.7219312191009521},{"id":"https://openalex.org/C6018138","wikidata":"https://www.wikidata.org/wiki/Q332715","display_name":"Absolutely convex set","level":5,"score":0.7039151191711426},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.643337607383728},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.5777524709701538},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5198310017585754},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5182871222496033},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.5123502016067505},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47380298376083374},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.46505364775657654},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4530446529388428},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.44221609830856323},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.4337017834186554},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.42716753482818604},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41874659061431885},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.41302046179771423},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.366491436958313},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.25739872455596924},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10477778315544128},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.053319185972213745},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10898-013-0051-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-013-0051-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-013-0051-4.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.1020.1783","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1020.1783","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.researchgate.net/profile/Kazimierz_Nikodem/publication/257588858_Strongly_convex_set-valued_maps/links/53ece7080cf26b9b7dbff9d8.pdf?origin%3Dpublication_detail","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.1023.238","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1023.238","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.researchgate.net/profile/Kazimierz_Nikodem/publication/257588858_Strongly_convex_set-valued_maps/links/53ece7080cf26b9b7dbff9d8.pdf","raw_type":"text"},{"id":"pmh:oai:RePEc:spr:jglopt:v:57:y:2013:i:3:p:695-705","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10898-013-0051-4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10898-013-0051-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-013-0051-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-013-0051-4.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1964224373.pdf","grobid_xml":"https://content.openalex.org/works/W1964224373.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W10589308","https://openalex.org/W95997959","https://openalex.org/W138374419","https://openalex.org/W257189624","https://openalex.org/W315148139","https://openalex.org/W753448919","https://openalex.org/W991172660","https://openalex.org/W1501503542","https://openalex.org/W1703448409","https://openalex.org/W1967922025","https://openalex.org/W1973613132","https://openalex.org/W1976938041","https://openalex.org/W1978407108","https://openalex.org/W1995222988","https://openalex.org/W2009062909","https://openalex.org/W2019761544","https://openalex.org/W2021394078","https://openalex.org/W2026160650","https://openalex.org/W2028005704","https://openalex.org/W2030128128","https://openalex.org/W2035648916","https://openalex.org/W2045443599","https://openalex.org/W2057113469","https://openalex.org/W2058667965","https://openalex.org/W2067684924","https://openalex.org/W2082858262","https://openalex.org/W2116598569","https://openalex.org/W2116773739","https://openalex.org/W2127909969","https://openalex.org/W2142506503","https://openalex.org/W2332703551","https://openalex.org/W2492408771","https://openalex.org/W2916728564","https://openalex.org/W2955198501","https://openalex.org/W4245290017","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3092518081","https://openalex.org/W2002037426","https://openalex.org/W2379830547","https://openalex.org/W2578380588","https://openalex.org/W4382519084","https://openalex.org/W2478309485","https://openalex.org/W2026600343","https://openalex.org/W2374624997","https://openalex.org/W4288640859","https://openalex.org/W1991697811"],"abstract_inverted_index":{"We":[0],"introduce":[1],"the":[2],"notion":[3],"of":[4,14,38,51],"strongly":[5,24,39,64,69],"$$t$$":[6,40],"-convex":[7,41],"set-valued":[8,26,42,66],"maps":[9,43,67],"and":[10,20,48,68],"present":[11],"some":[12],"properties":[13],"it.":[15],"In":[16],"particular,":[17],"a":[18,31,49,61],"Bernstein\u2013Doetsch":[19],"Sierpi\u0144ski-type":[21],"theorems":[22],"for":[23],"midconvex":[25],"maps,":[27],"as":[28,30],"well":[29],"Kuhn-type":[32],"result":[33],"are":[34],"obtained.":[35],"A":[36],"representation":[37,57],"in":[44],"inner":[45,52],"product":[46,53],"spaces":[47,54],"characterization":[50],"involving":[55],"this":[56],"is":[58,72],"given.":[59],"Finally,":[60],"connection":[62],"between":[63],"convex":[65,70],"sets":[71],"presented.":[73]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
