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Applications of N -Tupled Fixed Points in Partially Ordered Metric Spaces for Solving Systems of Nonlinear Matrix Equations

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  • Aynur Ali

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

  • Miroslav Hristov

    (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, 4000 Plovdiv, Bulgaria)

  • Hristina Kulina

    (Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria)

  • Boyan Zlatanov

    (Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria)

Abstract

We unify a known technique used for fixed points and coupled, tripled and N -tupled fixed points for weak monotone maps, i.e., maps that exhibit monotone properties for each of their variables. We weaken the classical contractive condition in partially ordered metric spaces by requiring it to hold only for a sequence of successive iterations, generated by the considered map, provided that it is a monotone one. We show that some known results are a direct consequence of the main result. The introduced technique shows that the partial order in the constructed Cartesian space is induced by both the partial order in the considered metric space and by the monotone properties of the investigated maps. We illustrate the main result, which is applied to solve a nonlinear matrix equation, following key ideas from Berzig, Duan & Samet. We present an illustrative example. We comment that a similar approach can be used to solve systems of nonlinear matrix equations.

Suggested Citation

  • Aynur Ali & Miroslav Hristov & Atanas Ilchev & Hristina Kulina & Boyan Zlatanov, 2025. "Applications of N -Tupled Fixed Points in Partially Ordered Metric Spaces for Solving Systems of Nonlinear Matrix Equations," Mathematics, MDPI, vol. 13(13), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2125-:d:1690296
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    References listed on IDEAS

    as
    1. Binayak S. Choudhury & Erdal Karapınar & Amaresh Kundu, 2012. "Tripled Coincidence Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-14, July.
    2. Marin Borcut & Mădălina Păcurar & Vasile Berinde, 2014. "Tripled Fixed Point Theorems for Mixed Monotone Kannan Type Contractive Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Tamer Nabil, 2019. "Krasnoselskii N-Tupled Fixed Point Theorem with Applications to Fractional Nonlinear Dynamical System," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-9, March.
    4. Engwerda, J.C., 1993. "On the existence of a positive definite solution of the matrix equation X = ATX-1A = I," Other publications TiSEM 9d762863-0dfe-4aeb-8a13-5, Tilburg University, School of Economics and Management.
    5. 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.
    6. Tamer Nabil, 2019. "Krasnoselskii N‐Tupled Fixed Point Theorem with Applications to Fractional Nonlinear Dynamical System," Advances in Mathematical Physics, John Wiley & Sons, vol. 2019(1).
    7. 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.
    8. Fahim Ud Din & Salha Alshaikey & Umar Ishtiaq & Muhammad Din & Salvatore Sessa, 2024. "Single and Multi-Valued Ordered-Theoretic Perov Fixed-Point Results for θ -Contraction with Application to Nonlinear System of Matrix Equations," Mathematics, MDPI, vol. 12(9), pages 1-15, April.
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