{"id":"https://openalex.org/W2739424486","doi":"https://doi.org/10.1007/s11590-017-1174-1","title":"An elementary proof of the quadratic envelope characterization of zero-derivative points","display_name":"An elementary proof of the quadratic envelope characterization of zero-derivative points","publication_year":2017,"publication_date":"2017-07-22","ids":{"openalex":"https://openalex.org/W2739424486","doi":"https://doi.org/10.1007/s11590-017-1174-1","mag":"2739424486"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-017-1174-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-017-1174-1","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","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/A5032876207","display_name":"Dragan Juki\u0107","orcid":"https://orcid.org/0000-0003-0215-3687"},"institutions":[{"id":"https://openalex.org/I51314090","display_name":"University of Osijek","ror":"https://ror.org/05sw4wc49","country_code":"HR","type":"education","lineage":["https://openalex.org/I51314090"]}],"countries":["HR"],"is_corresponding":true,"raw_author_name":"Dragan Juki\u0107","raw_affiliation_strings":["Department of Mathematics, J.J. Strossmayer University of Osijek, Trg Ljudevita Gaja 6, 31 000, Osijek, Croatia"],"raw_orcid":"https://orcid.org/0000-0003-0215-3687","affiliations":[{"raw_affiliation_string":"Department of Mathematics, J.J. Strossmayer University of Osijek, Trg Ljudevita Gaja 6, 31 000, Osijek, Croatia","institution_ids":["https://openalex.org/I51314090"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032876207"],"corresponding_institution_ids":["https://openalex.org/I51314090"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17287275,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"5","first_page":"1155","last_page":"1156"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9819999933242798,"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/T12504","display_name":"Mathematics and Applications","score":0.9819999933242798,"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":0.9710999727249146,"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":0.9696000218391418,"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/zero","display_name":"Zero (linguistics)","score":0.6631348133087158},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6525288224220276},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6500673294067383},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.6455544829368591},{"id":"https://openalex.org/keywords/elementary-proof","display_name":"Elementary proof","score":0.6253657341003418},{"id":"https://openalex.org/keywords/envelope","display_name":"Envelope (radar)","score":0.6132562160491943},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6017556190490723},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5650076270103455},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5431825518608093},{"id":"https://openalex.org/keywords/fr\u00e9chet-derivative","display_name":"Fr\u00e9chet derivative","score":0.4218323230743408},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4034227132797241},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3680065870285034},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35758069157600403},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33598649501800537},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17985177040100098},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13323870301246643},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10729140043258667}],"concepts":[{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6631348133087158},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6525288224220276},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6500673294067383},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.6455544829368591},{"id":"https://openalex.org/C2777478746","wikidata":"https://www.wikidata.org/wiki/Q5358910","display_name":"Elementary proof","level":2,"score":0.6253657341003418},{"id":"https://openalex.org/C65155139","wikidata":"https://www.wikidata.org/wiki/Q5380912","display_name":"Envelope (radar)","level":3,"score":0.6132562160491943},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6017556190490723},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5650076270103455},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5431825518608093},{"id":"https://openalex.org/C118335899","wikidata":"https://www.wikidata.org/wiki/Q1305350","display_name":"Fr\u00e9chet derivative","level":3,"score":0.4218323230743408},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4034227132797241},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3680065870285034},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35758069157600403},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33598649501800537},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17985177040100098},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13323870301246643},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10729140043258667},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11590-017-1174-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-017-1174-1","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322674","display_name":"Hrvatska Zaklada za Znanost","ror":"https://ror.org/03n51vw80"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1438684603","https://openalex.org/W1967710355","https://openalex.org/W2120023939"],"related_works":["https://openalex.org/W1983139135","https://openalex.org/W4248651406","https://openalex.org/W40430404","https://openalex.org/W4306294781","https://openalex.org/W2766857374","https://openalex.org/W2387031683","https://openalex.org/W3046356091","https://openalex.org/W2962978177","https://openalex.org/W2788728502","https://openalex.org/W2386753794"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}