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

Aynur Ali, Miroslav Hristov, 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
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

Mathematics, 2025, vol. 13, issue 13, 1-20

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.

Keywords: n -tupled 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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