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

Ali, Aynur; Hristov, Miroslav; Ilchev, Atanas; Kulina, Hristina; Zlatanov, Boyan

doi:10.3390/math13132125

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Open AccessFeature PaperArticle

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

by

Aynur Ali

¹

,

Miroslav Hristov

¹

,

Atanas Ilchev

^2,*

,

Hristina Kulina

²

and

Boyan Zlatanov

²

¹

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

²

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

^*

Author to whom correspondence should be addressed.

Mathematics 2025, 13(13), 2125; https://doi.org/10.3390/math13132125

Submission received: 24 May 2025 / Revised: 12 June 2025 / Accepted: 25 June 2025 / Published: 29 June 2025

(This article belongs to the Special Issue Advanced Research in Functional Analysis and Operator Theory)

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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

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MDPI and ACS Style

Ali, A.; Hristov, M.; Ilchev, A.; Kulina, H.; Zlatanov, B. Applications of N-Tupled Fixed Points in Partially Ordered Metric Spaces for Solving Systems of Nonlinear Matrix Equations. Mathematics 2025, 13, 2125. https://doi.org/10.3390/math13132125

AMA Style

Ali A, Hristov M, Ilchev A, Kulina H, Zlatanov B. Applications of N-Tupled Fixed Points in Partially Ordered Metric Spaces for Solving Systems of Nonlinear Matrix Equations. Mathematics. 2025; 13(13):2125. https://doi.org/10.3390/math13132125

Chicago/Turabian Style

Ali, Aynur, Miroslav Hristov, Atanas Ilchev, Hristina Kulina, and Boyan Zlatanov. 2025. "Applications of N-Tupled Fixed Points in Partially Ordered Metric Spaces for Solving Systems of Nonlinear Matrix Equations" Mathematics 13, no. 13: 2125. https://doi.org/10.3390/math13132125

APA Style

Ali, A., Hristov, M., Ilchev, A., Kulina, H., & Zlatanov, B. (2025). Applications of N-Tupled Fixed Points in Partially Ordered Metric Spaces for Solving Systems of Nonlinear Matrix Equations. Mathematics, 13(13), 2125. https://doi.org/10.3390/math13132125

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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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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