{"id":"https://openalex.org/W2979416550","doi":"https://doi.org/10.3390/axioms8040114","title":"Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable\u2014Part II: Extremal Points, Convexity, Periodicity","display_name":"Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable\u2014Part II: Extremal Points, Convexity, Periodicity","publication_year":2019,"publication_date":"2019-10-14","ids":{"openalex":"https://openalex.org/W2979416550","doi":"https://doi.org/10.3390/axioms8040114","mag":"2979416550"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms8040114","pdf_url":"https://www.mdpi.com/2075-1680/8/4/114/pdf?version=1571048036","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_indexed_in_scopus":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/8/4/114/pdf?version=1571048036","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084200898","display_name":"Luciano Stefanini","orcid":"https://orcid.org/0000-0002-7367-8520"},"institutions":[{"id":"https://openalex.org/I190397597","display_name":"University of Urbino","ror":"https://ror.org/04q4kt073","country_code":"IT","type":"funder","lineage":["https://openalex.org/I190397597"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Luciano Stefanini","raw_affiliation_strings":["Department of Economics, Society, Politics, University of Urbino Carlo Bo, Via A. Saffi 42, 61029 Urbino, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Economics, Society, Politics, University of Urbino Carlo Bo, Via A. Saffi 42, 61029 Urbino, Italy","institution_ids":["https://openalex.org/I190397597"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056967799","display_name":"Laerte Sorini","orcid":"https://orcid.org/0000-0003-0088-4005"},"institutions":[{"id":"https://openalex.org/I190397597","display_name":"University of Urbino","ror":"https://ror.org/04q4kt073","country_code":"IT","type":"funder","lineage":["https://openalex.org/I190397597"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Laerte Sorini","raw_affiliation_strings":["Department of Economics, Society, Politics, University of Urbino Carlo Bo, Via A. Saffi 42, 61029 Urbino, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Economics, Society, Politics, University of Urbino Carlo Bo, Via A. Saffi 42, 61029 Urbino, Italy","institution_ids":["https://openalex.org/I190397597"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079360809","display_name":"Benedetta Amicizia","orcid":"https://orcid.org/0000-0003-3003-8133"},"institutions":[{"id":"https://openalex.org/I190397597","display_name":"University of Urbino","ror":"https://ror.org/04q4kt073","country_code":"IT","type":"funder","lineage":["https://openalex.org/I190397597"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Benedetta Amicizia","raw_affiliation_strings":["Department of Economics, Society, Politics, University of Urbino Carlo Bo, Via A. Saffi 42, 61029 Urbino, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Economics, Society, Politics, University of Urbino Carlo Bo, Via A. Saffi 42, 61029 Urbino, Italy","institution_ids":["https://openalex.org/I190397597"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5084200898"],"corresponding_institution_ids":["https://openalex.org/I190397597"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.357,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":10,"citation_normalized_percentile":{"value":0.793903,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":85,"max":86},"biblio":{"volume":"8","issue":"4","first_page":"114","last_page":"114"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9997,"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"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9997,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9962,"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":0.9935,"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/convexity","display_name":"Convexity","score":0.79007435},{"id":"https://openalex.org/keywords/midpoint","display_name":"Midpoint","score":0.7115106},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.4451366}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.79007435},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7549919},{"id":"https://openalex.org/C34130140","wikidata":"https://www.wikidata.org/wiki/Q1645406","display_name":"Midpoint","level":2,"score":0.7115106},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6837771},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6835577},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.60481864},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.48656455},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.46232063},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.4451366},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36306095},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33182138},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3242793},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22914955},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18740466},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.13528651},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"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}],"mesh":[],"locations_count":2,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms8040114","pdf_url":"https://www.mdpi.com/2075-1680/8/4/114/pdf?version=1571048036","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_indexed_in_scopus":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":false,"landing_page_url":"https://doaj.org/article/2581ba0f72724517bb20ca902c3c35b8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms8040114","pdf_url":"https://www.mdpi.com/2075-1680/8/4/114/pdf?version=1571048036","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_indexed_in_scopus":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":35,"referenced_works":["https://openalex.org/W1507872748","https://openalex.org/W1542253753","https://openalex.org/W1577634535","https://openalex.org/W1580809199","https://openalex.org/W1583370286","https://openalex.org/W1964914499","https://openalex.org/W1986928005","https://openalex.org/W1995123739","https://openalex.org/W2001359285","https://openalex.org/W2006748591","https://openalex.org/W2013367574","https://openalex.org/W2013934519","https://openalex.org/W2034038007","https://openalex.org/W2038354216","https://openalex.org/W2038849562","https://openalex.org/W2050676121","https://openalex.org/W2059728681","https://openalex.org/W2063970263","https://openalex.org/W2070545443","https://openalex.org/W2176210190","https://openalex.org/W2235457012","https://openalex.org/W228864768","https://openalex.org/W2299040064","https://openalex.org/W2748397051","https://openalex.org/W2783252215","https://openalex.org/W2799868560","https://openalex.org/W2801266866","https://openalex.org/W2941585389","https://openalex.org/W2953446726","https://openalex.org/W2979728612","https://openalex.org/W4254489622","https://openalex.org/W565587792","https://openalex.org/W569706131","https://openalex.org/W575976088","https://openalex.org/W636069421"],"related_works":["https://openalex.org/W4401666157","https://openalex.org/W4389849086","https://openalex.org/W4292074540","https://openalex.org/W4281957576","https://openalex.org/W3130449832","https://openalex.org/W3003767881","https://openalex.org/W2361785418","https://openalex.org/W2164621095","https://openalex.org/W2005013113","https://openalex.org/W1996226968"],"abstract_inverted_index":{"We":[0,18,58,76],"continue":[1],"the":[2,8,22,39,70,88,100,114],"presentation":[3],"of":[4,13,28,35,41,62,85,90,102],"new":[5],"results":[6,23,49],"in":[7,25,38,97],"calculus":[9],"for":[10,73],"interval-valued":[11,91,103],"functions":[12,92,104],"a":[14,32],"single":[15],"real":[16],"variable.":[17],"start":[19],"here":[20],"with":[21,82],"presented":[24],"part":[26],"I":[27],"this":[29],"paper,":[30],"namely,":[31],"general":[33],"setting":[34],"partial":[36],"orders":[37],"space":[40],"compact":[42],"intervals":[43],"(in":[44],"midpoint-radius":[45],"representation)":[46],"and":[47,52,56,65,68,87,95,107,111],"basic":[48,71],"on":[50],"convergence":[51],"limits,":[53],"continuity,":[54],"gH-differentiability,":[55],"monotonicity.":[57],"define":[59],"different":[60],"types":[61],"(local)":[63],"minimal":[64],"maximal":[66],"points":[67],"develop":[69],"theory":[72],"their":[74],"characterization.":[75],"then":[77],"consider":[78],"some":[79],"interesting":[80],"connections":[81],"applied":[83],"geometry":[84],"curves":[86],"convexity":[89],"is":[93,105],"introduced":[94],"analyzed":[96],"detail.":[98],"Further,":[99],"periodicity":[101],"described":[106],"analyzed.":[108],"Several":[109],"examples":[110],"pictures":[112],"accompany":[113],"presentation.":[115]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2979416550","counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4}],"updated_date":"2025-03-17T01:50:13.978529","created_date":"2019-10-18"}