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Volume 10
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Article

Applications of Coupled Fixed Points for Multivalued Maps in the Equilibrium in Duopoly Markets and in Aquatic Ecosystems

by
Gana Gecheva
1,
Miroslav Hristov
2,*,
Diana Nedelcheva
3,
Margarita Ruseva
4 and
Boyan Zlatanov
5
1
Department of Ecology and Environmental Conservation, Faculty of Biology, University of Plovdiv “Paisii Hilendarski”, 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria
2
Department of Algebra and Geometry, Faculty of Mathematics and Computer Science, University of Shumen “Konstantin Preslavsky”, 115 Universitetska Str., 9700 Shumen, Bulgaria
3
Department of Mathematics and Physics, Faculty of Electrical Engineering, Technical University of Varna, 1 Studentska Str., 9000 Varna, Bulgaria
4
Department of Management and Quantitative Economicsx, Faculty of Economics and Social Sciences, University of Plovdiv “Paisii Hilendarski”, 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria
5
Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv “Paisii Hilendarski”, 24 Tzar Assen Str., 4000 Plovdiv, Bulgaria
*
Author to whom correspondence should be addressed.
Axioms 2021, 10(2), 44; https://doi.org/10.3390/axioms10020044
Submission received: 25 February 2021 / Revised: 20 March 2021 / Accepted: 22 March 2021 / Published: 26 March 2021
(This article belongs to the Special Issue Theory and Application of Fixed Point)
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Abstract

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.
Keywords: multivalued maps; coupled fixed points; equilibrium multivalued maps; coupled fixed points; equilibrium

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MDPI and ACS Style

Gecheva, G.; Hristov, M.; Nedelcheva, D.; Ruseva, M.; Zlatanov, B. Applications of Coupled Fixed Points for Multivalued Maps in the Equilibrium in Duopoly Markets and in Aquatic Ecosystems. Axioms 2021, 10, 44. https://doi.org/10.3390/axioms10020044

AMA Style

Gecheva G, Hristov M, Nedelcheva D, Ruseva M, Zlatanov B. Applications of Coupled Fixed Points for Multivalued Maps in the Equilibrium in Duopoly Markets and in Aquatic Ecosystems. Axioms. 2021; 10(2):44. https://doi.org/10.3390/axioms10020044

Chicago/Turabian Style

Gecheva, Gana, Miroslav Hristov, Diana Nedelcheva, Margarita Ruseva, and Boyan Zlatanov. 2021. "Applications of Coupled Fixed Points for Multivalued Maps in the Equilibrium in Duopoly Markets and in Aquatic Ecosystems" Axioms 10, no. 2: 44. https://doi.org/10.3390/axioms10020044

APA Style

Gecheva, G., Hristov, M., Nedelcheva, D., Ruseva, M., & Zlatanov, B. (2021). Applications of Coupled Fixed Points for Multivalued Maps in the Equilibrium in Duopoly Markets and in Aquatic Ecosystems. Axioms, 10(2), 44. https://doi.org/10.3390/axioms10020044

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