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

Aynur Ali, Cvetelina Dinkova, Atanas Ilchev, Hristina Kulina () and Boyan Zlatanov
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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
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

Mathematics, 2025, vol. 13, issue 5, 1-26

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.

Keywords: coupled fixed points; partially ordered metric space; mixed monotone property; matrix equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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