{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T09:46:35Z","timestamp":1777542395339,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,3,26]],"date-time":"2021-03-26T00:00:00Z","timestamp":1616716800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We have obtained a new class of ordered pairs of multivalued maps that have pairs of coupled fixed points. We illustrate the main result with two examples that cover a wide range of models. We apply the main result in models in duopoly markets to get a market equilibrium and in aquatic ecosystems, also to get an equilibrium.<\/jats:p>","DOI":"10.3390\/axioms10020044","type":"journal-article","created":{"date-parts":[[2021,3,26]],"date-time":"2021-03-26T13:17:53Z","timestamp":1616764673000},"page":"44","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Applications of Coupled Fixed Points for Multivalued Maps in the Equilibrium in Duopoly Markets and in Aquatic Ecosystems"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5747-255X","authenticated-orcid":false,"given":"Gana","family":"Gecheva","sequence":"first","affiliation":[{"name":"Department of Ecology and Environmental Conservation, Faculty of Biology, University of Plovdiv \u201cPaisii Hilendarski\u201d, 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6475-6267","authenticated-orcid":false,"given":"Miroslav","family":"Hristov","sequence":"additional","affiliation":[{"name":"Department of Algebra and Geometry, Faculty of Mathematics and Computer Science, University of Shumen \u201cKonstantin Preslavsky\u201d, 115 Universitetska Str., 9700 Shumen, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6094-7595","authenticated-orcid":false,"given":"Diana","family":"Nedelcheva","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Physics, Faculty of Electrical Engineering, Technical University of Varna, 1 Studentska Str., 9000 Varna, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8683-051X","authenticated-orcid":false,"given":"Margarita","family":"Ruseva","sequence":"additional","affiliation":[{"name":"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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5857-9372","authenticated-orcid":false,"given":"Boyan","family":"Zlatanov","sequence":"additional","affiliation":[{"name":"Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv \u201cPaisii Hilendarski\u201d, 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"475","DOI":"10.2140\/pjm.1969.30.475","article-title":"Multi\u2013Valued Contraction Mappings","volume":"30","author":"Nadler","year":"1969","journal-title":"Pac. 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