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On Coupled Best Proximity Points in Reflexive Banach Spaces

Author

Listed:
  • 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)

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.

Suggested Citation

  • Laura Ajeti & Atanas Ilchev & Boyan Zlatanov, 2022. "On Coupled Best Proximity Points in Reflexive Banach Spaces," Mathematics, MDPI, vol. 10(8), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1304-:d:793837
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    References listed on IDEAS

    as
    1. Akio Matsumoto & Ferenc Szidarovszky, 2018. "Dynamic Oligopolies with Time Delays," Springer Books, Springer, number 978-981-13-1786-6, December.
    2. Yulia Dzhabarova & Stanimir Kabaivanov & Margarita Ruseva & Boyan Zlatanov, 2020. "Existence, Uniqueness and Stability of Market Equilibrium in Oligopoly Markets," Administrative Sciences, MDPI, vol. 10(3), pages 1-32, September.
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