Bhaskar-Lakshmikantham fixed point theorem vs Ran-Reunrings one and some possible generalizations and applications in matrix equations

Aynur Ali; Cvetelina Dinkova; Atanas Ilchev; Boyan Zlatanov; Aynur Ali; Cvetelina Dinkova; Atanas Ilchev; Boyan Zlatanov

doi:10.3934/math.20241064

AIMS Mathematics

2024, Volume 9, Issue 8: 21890-21917. doi: 10.3934/math.20241064

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Research article

Bhaskar-Lakshmikantham fixed point theorem vs Ran-Reunrings one and some possible generalizations and applications in matrix equations

1.
Faculty of Mathematics and Informatics, Konstantin Preslavsky University of Shumen, 115 Universitetska Str., Shumen 9700, Bulgaria
2.
Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 "Tzar Assen Str.", Plovdiv 4000, Bulgaria

Received: 21 April 2024 Revised: 28 May 2024 Accepted: 12 June 2024 Published: 10 July 2024
MSC : 15A24, 65H05

We provided a generalization of the existence and uniqueness of fixed points in partially ordered metric spaces for a monotone map. We applied the major results in the investigation of coupled fixed points for ordered pairs of two maps that met various monotone features, which included a mixed monotone property or a total monotone property. To ascertain necessary requirements for the existence and uniqueness of solutions to systems of matrix equations, the results regarding coupled fixed points for ordered pairs of maps were utilized. These results are illustrated with numerical examples. Some of the known results are a consequence of the results we obtained.
- coupled fixed points,
- partially ordered metric space,
- mixed monotone property,
- matrix equations
Citation: Aynur Ali, Cvetelina Dinkova, Atanas Ilchev, Boyan Zlatanov. Bhaskar-Lakshmikantham fixed point theorem vs Ran-Reunrings one and some possible generalizations and applications in matrix equations[J]. AIMS Mathematics, 2024, 9(8): 21890-21917. doi: 10.3934/math.20241064

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Abstract

We provided a generalization of the existence and uniqueness of fixed points in partially ordered metric spaces for a monotone map. We applied the major results in the investigation of coupled fixed points for ordered pairs of two maps that met various monotone features, which included a mixed monotone property or a total monotone property. To ascertain necessary requirements for the existence and uniqueness of solutions to systems of matrix equations, the results regarding coupled fixed points for ordered pairs of maps were utilized. These results are illustrated with numerical examples. Some of the known results are a consequence of the results we obtained.

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