{"id":"https://openalex.org/W3141665753","doi":"https://doi.org/10.3390/axioms10020044","title":"Applications of Coupled Fixed Points for Multivalued Maps in the Equilibrium in Duopoly Markets and in Aquatic Ecosystems","display_name":"Applications of Coupled Fixed Points for Multivalued Maps in the Equilibrium in Duopoly Markets and in Aquatic Ecosystems","publication_year":2021,"publication_date":"2021-03-26","ids":{"openalex":"https://openalex.org/W3141665753","doi":"https://doi.org/10.3390/axioms10020044","mag":"3141665753"},"language":"en","primary_location":{"id":"doi:10.3390/axioms10020044","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10020044","pdf_url":"https://www.mdpi.com/2075-1680/10/2/44/pdf?version=1617937159","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/10/2/44/pdf?version=1617937159","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015385601","display_name":"Gana Gecheva","orcid":"https://orcid.org/0000-0001-5747-255X"},"institutions":[{"id":"https://openalex.org/I192878625","display_name":"Plovdiv University","ror":"https://ror.org/0545p3742","country_code":"BG","type":"education","lineage":["https://openalex.org/I192878625"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Gana Gecheva","raw_affiliation_strings":["Department of Ecology and Environmental Conservation, Faculty of Biology, University of Plovdiv \u201cPaisii Hilendarski\u201d, 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria","Department of Ecology and Environmental Conservation, Faculty of Biology, University of Plovdiv \"Paisii Hilendarski\", 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria"],"raw_orcid":"https://orcid.org/0000-0001-5747-255X","affiliations":[{"raw_affiliation_string":"Department of Ecology and Environmental Conservation, Faculty of Biology, University of Plovdiv \u201cPaisii Hilendarski\u201d, 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria","institution_ids":["https://openalex.org/I192878625"]},{"raw_affiliation_string":"Department of Ecology and Environmental Conservation, Faculty of Biology, University of Plovdiv \"Paisii Hilendarski\", 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria","institution_ids":["https://openalex.org/I192878625"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031791996","display_name":"Miroslav Hristov","orcid":"https://orcid.org/0000-0002-6475-6267"},"institutions":[{"id":"https://openalex.org/I39995536","display_name":"Shumen University","ror":"https://ror.org/03yht3k11","country_code":"BG","type":"education","lineage":["https://openalex.org/I39995536"]}],"countries":["BG"],"is_corresponding":true,"raw_author_name":"Miroslav Hristov","raw_affiliation_strings":["Department of Algebra and Geometry, Faculty of Mathematics and Computer Science, University of Shumen \u201cKonstantin Preslavsky\u201d, 115 Universitetska Str., 9700 Shumen, Bulgaria","Department of Algebra and Geometry, Faculty of Mathematics and Computer Science, University of Shumen \"Konstantin Preslavsky\", 115 Universitetska Str., 9700 Shumen, Bulgaria"],"raw_orcid":"https://orcid.org/0000-0002-6475-6267","affiliations":[{"raw_affiliation_string":"Department of Algebra and Geometry, Faculty of Mathematics and Computer Science, University of Shumen \u201cKonstantin Preslavsky\u201d, 115 Universitetska Str., 9700 Shumen, Bulgaria","institution_ids":["https://openalex.org/I39995536"]},{"raw_affiliation_string":"Department of Algebra and Geometry, Faculty of Mathematics and Computer Science, University of Shumen \"Konstantin Preslavsky\", 115 Universitetska Str., 9700 Shumen, Bulgaria","institution_ids":["https://openalex.org/I39995536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012298591","display_name":"Diana Nedelcheva","orcid":"https://orcid.org/0000-0001-6094-7595"},"institutions":[{"id":"https://openalex.org/I147527907","display_name":"Technical University of Varna","ror":"https://ror.org/03zrwm897","country_code":"BG","type":"education","lineage":["https://openalex.org/I147527907"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Diana Nedelcheva","raw_affiliation_strings":["Department of Mathematics and Physics, Faculty of Electrical Engineering, Technical University of Varna, 1 Studentska Str., 9000 Varna, Bulgaria"],"raw_orcid":"https://orcid.org/0000-0001-6094-7595","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, Faculty of Electrical Engineering, Technical University of Varna, 1 Studentska Str., 9000 Varna, Bulgaria","institution_ids":["https://openalex.org/I147527907"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068677765","display_name":"Margarita Ruseva","orcid":"https://orcid.org/0000-0002-8683-051X"},"institutions":[{"id":"https://openalex.org/I192878625","display_name":"Plovdiv University","ror":"https://ror.org/0545p3742","country_code":"BG","type":"education","lineage":["https://openalex.org/I192878625"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Margarita Ruseva","raw_affiliation_strings":["Department of Management and Quantitative Economicsx, Faculty of Economics and Social Sciences, University of Plovdiv \u201cPaisii Hilendarski\u201d, 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria","Department of Management and Quantitative Economicsx, Faculty of Economics and Social Sciences, University of Plovdiv \"Paisii Hilendarski\", 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria"],"raw_orcid":"https://orcid.org/0000-0002-8683-051X","affiliations":[{"raw_affiliation_string":"Department of Management and Quantitative Economicsx, Faculty of Economics and Social Sciences, University of Plovdiv \u201cPaisii Hilendarski\u201d, 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria","institution_ids":["https://openalex.org/I192878625"]},{"raw_affiliation_string":"Department of Management and Quantitative Economicsx, Faculty of Economics and Social Sciences, University of Plovdiv \"Paisii Hilendarski\", 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria","institution_ids":["https://openalex.org/I192878625"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010014944","display_name":"Boyan Zlatanov","orcid":"https://orcid.org/0000-0002-5857-9372"},"institutions":[{"id":"https://openalex.org/I192878625","display_name":"Plovdiv University","ror":"https://ror.org/0545p3742","country_code":"BG","type":"education","lineage":["https://openalex.org/I192878625"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Boyan Zlatanov","raw_affiliation_strings":["Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv \u201cPaisii Hilendarski\u201d, 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria","Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv \"Paisii Hilendarski\", 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria"],"raw_orcid":"https://orcid.org/0000-0002-5857-9372","affiliations":[{"raw_affiliation_string":"Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv \u201cPaisii Hilendarski\u201d, 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria","institution_ids":["https://openalex.org/I192878625"]},{"raw_affiliation_string":"Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv \"Paisii Hilendarski\", 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria","institution_ids":["https://openalex.org/I192878625"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5031791996"],"corresponding_institution_ids":["https://openalex.org/I39995536"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":4.0234,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.94350007,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"10","issue":"2","first_page":"44","last_page":"44"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9965999722480774,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9785000085830688,"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/duopoly","display_name":"Duopoly","score":0.8604371547698975},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.5400960445404053},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.5374959111213684},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5152857303619385},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5015683174133301},{"id":"https://openalex.org/keywords/ecosystem","display_name":"Ecosystem","score":0.46685272455215454},{"id":"https://openalex.org/keywords/aquatic-ecosystem","display_name":"Aquatic ecosystem","score":0.43978190422058105},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.37461575865745544},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32972362637519836},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.329349160194397},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.32417961955070496},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28228816390037537},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.15835589170455933},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09146386384963989},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.058398157358169556}],"concepts":[{"id":"https://openalex.org/C180456769","wikidata":"https://www.wikidata.org/wiki/Q750207","display_name":"Duopoly","level":3,"score":0.8604371547698975},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5400960445404053},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.5374959111213684},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5152857303619385},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5015683174133301},{"id":"https://openalex.org/C110872660","wikidata":"https://www.wikidata.org/wiki/Q37813","display_name":"Ecosystem","level":2,"score":0.46685272455215454},{"id":"https://openalex.org/C175327387","wikidata":"https://www.wikidata.org/wiki/Q3289906","display_name":"Aquatic ecosystem","level":2,"score":0.43978190422058105},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.37461575865745544},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32972362637519836},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.329349160194397},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.32417961955070496},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28228816390037537},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.15835589170455933},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09146386384963989},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.058398157358169556},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C16520705","wikidata":"https://www.wikidata.org/wiki/Q601799","display_name":"Cournot competition","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms10020044","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10020044","pdf_url":"https://www.mdpi.com/2075-1680/10/2/44/pdf?version=1617937159","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:88681a4113c74c66b0f3cb5841ad8ce0","is_oa":true,"landing_page_url":"https://doaj.org/article/88681a4113c74c66b0f3cb5841ad8ce0","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":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 10, Iss 2, p 44 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/10/2/44/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms10020044","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 10; Issue 2; Pages: 44","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms10020044","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10020044","pdf_url":"https://www.mdpi.com/2075-1680/10/2/44/pdf?version=1617937159","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.5600000023841858,"display_name":"Life in Land"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320330331","display_name":"Constantine of Preslav University of Shumen","ror":"https://ror.org/03yht3k11"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3141665753.pdf","grobid_xml":"https://content.openalex.org/works/W3141665753.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W99187563","https://openalex.org/W1554154521","https://openalex.org/W1965421426","https://openalex.org/W1968577377","https://openalex.org/W1991568184","https://openalex.org/W2049175562","https://openalex.org/W2122440577","https://openalex.org/W2129941846","https://openalex.org/W2898732977","https://openalex.org/W2990133946","https://openalex.org/W3021910509","https://openalex.org/W3025770671","https://openalex.org/W3037599300","https://openalex.org/W3042998632","https://openalex.org/W3047492310","https://openalex.org/W3083105732","https://openalex.org/W3083250889","https://openalex.org/W3083532042","https://openalex.org/W3092168880","https://openalex.org/W3093333762","https://openalex.org/W3094835310","https://openalex.org/W3095995788","https://openalex.org/W3102097931","https://openalex.org/W3119687714","https://openalex.org/W4241339016","https://openalex.org/W6604081106","https://openalex.org/W6770791517","https://openalex.org/W6777600700"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2164415648","https://openalex.org/W1967103436","https://openalex.org/W1990941443","https://openalex.org/W2897123541","https://openalex.org/W170161335","https://openalex.org/W2233463112","https://openalex.org/W1979478303","https://openalex.org/W2528959248","https://openalex.org/W2591935376"],"abstract_inverted_index":{"We":[0,19,34],"have":[1,13],"obtained":[2],"a":[3,29,46],"new":[4],"class":[5],"of":[6,9,15,32],"ordered":[7],"pairs":[8,14],"multivalued":[10],"maps":[11],"that":[12,27],"coupled":[16],"fixed":[17],"points.":[18],"illustrate":[20],"the":[21,36],"main":[22,37],"result":[23,38],"with":[24],"two":[25],"examples":[26],"cover":[28],"wide":[30],"range":[31],"models.":[33],"apply":[35],"in":[39,41,50],"models":[40],"duopoly":[42],"markets":[43],"to":[44,54],"get":[45,55],"market":[47],"equilibrium":[48],"and":[49],"aquatic":[51],"ecosystems,":[52],"also":[53],"an":[56],"equilibrium.":[57]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2021-04-13T00:00:00"}
