On Coupled Best Proximity Points in Reflexive Banach Spaces

Laura Ajeti, Atanas Ilchev and Boyan Zlatanov
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Laura Ajeti: Faculty of Mathematics and Informatics, University of Plovdiv “Paisii Hilendarski”, 24, Tsar Assen Str., 4000 Plovdiv, Bulgaria
Atanas Ilchev: Faculty of Mathematics and Informatics, University of Plovdiv “Paisii Hilendarski”, 24, Tsar Assen Str., 4000 Plovdiv, Bulgaria
Boyan Zlatanov: Faculty of Mathematics and Informatics, University of Plovdiv “Paisii Hilendarski”, 24, Tsar Assen Str., 4000 Plovdiv, Bulgaria

Mathematics, 2022, vol. 10, issue 8, 1-19

Abstract: We investigated the existence and uniqueness of coupled best proximity points for some cyclic and semi-cyclic maps in a reflexive Banach space. We found sufficient conditions, ensuring the existence of coupled best proximity points in reflexive Banach spaces and some convexity types of conditions, ensuring uniqueness of the coupled best proximity points in strictly convex Banach spaces. We illustrate the results with examples and we present an application of one of the theorems in the modeling of duopoly markets, to have an existence of market equilibrium. We show that, in general, the iterative sequences can have chaotic behavior.

Keywords: reflexive Banach spaces; coupled best proximity point; cyclic maps; oligopoly markets; market equilibrium (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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