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Tripled Fixed Points, Obtained by Ran-Reunrings Theorem for Monotone Maps in Partially Ordered Metric Spaces

Author

Listed:
  • Aynur Ali

    (Department of Algebra and Geometry, Faculty of Mathematics and Informatics, Konstantin Preslavsky University of Shumen, 115 Universitetska Str., 9700 Shumen, Bulgaria)

  • Cvetelina Dinkova

    (Department of Algebra and Geometry, Faculty of Mathematics and Informatics, Konstantin Preslavsky University of Shumen, 115 Universitetska Str., 9700 Shumen, Bulgaria)

  • Atanas Ilchev

    (Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tsar Assen Str., 4000 Plovdiv, Bulgaria)

  • Hristina Kulina

    (Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tsar Assen Str., 4000 Plovdiv, Bulgaria)

  • Boyan Zlatanov

    (Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tsar Assen Str., 4000 Plovdiv, Bulgaria)

Abstract

Using the deep result of Ran & Reunrings, we generalize existing results for tripled fixed points. In contrast to the previously known results for tripled fixed points of maps with or without the mixed monotone property in partially ordered complete metric spaces, we demonstrate that it is possible to obtain results for the existence and uniqueness of such points for arbitrary maps with a type of monotonicity, with the partial ordering in the Cartesian product arising from the maps itself. We prove theorems that ensure the existence and uniqueness for tripled fixed points for maps with different types of monotone properties. We obtain sufficient conditions for the existence and uniqueness of systems of three nonlinear matrix equations. The obtained results are illustrated by solving systems of matrix equations.

Suggested Citation

  • Aynur Ali & Cvetelina Dinkova & Atanas Ilchev & Hristina Kulina & Boyan Zlatanov, 2025. "Tripled Fixed Points, Obtained by Ran-Reunrings Theorem for Monotone Maps in Partially Ordered Metric Spaces," Mathematics, MDPI, vol. 13(5), pages 1-26, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:760-:d:1599658
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    References listed on IDEAS

    as
    1. Atanas Ilchev & Vanya Ivanova & Hristina Kulina & Polina Yaneva & Boyan Zlatanov, 2024. "Investigation of Equilibrium in Oligopoly Markets with the Help of Tripled Fixed Points in Banach Spaces," Econometrics, MDPI, vol. 12(2), pages 1-24, June.
    2. Marin Borcut & Mădălina Păcurar & Vasile Berinde, 2014. "Tripled Fixed Point Theorems for Mixed Monotone Kannan Type Contractive Mappings," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, March.
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