On the multivalued $ \rho _{\ast } $-interpolative contractions in fuzzy metric spaces with application to nonlinear matrix equations

Müzeyyen Sangurlu Sezen; Mohammed Jasim Mohammed; Sina Etemad; Jessada Tariboon; Müzeyyen Sangurlu Sezen; Mohammed Jasim Mohammed; Sina Etemad; Jessada Tariboon

doi:10.3934/math.2026171

AIMS Mathematics

2026, Volume 11, Issue 2: 4263-4282. doi: 10.3934/math.2026171

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Research article

On the multivalued $ \rho _{\ast } $-interpolative contractions in fuzzy metric spaces with application to nonlinear matrix equations

1.
Department of Mathematics, Faculty of Sciences, Gazi University, Ankara, Turkey
2.
Department of Mathematics, College of Science, University of Anbar, Ramadi 31001, Iraq
3.
Institute of Graduate Studies and Research, Cyprus International University, Nicosia, Northern Cyprus, via Mersin 10, Turkey
4.
Jadara Research Center, Jadara University, Irbid 21110, Jordan
5.
Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand

Received: 28 September 2025 Revised: 01 February 2026 Accepted: 03 February 2026 Published: 11 February 2026
MSC : 47H10, 54H25

In this study, the subject of the multivalued $ \rho _{\ast } $-interpolative Ćirić-Reich-Rus-type fuzzy contractions is introduced and investigated in which the $ \vartheta $-comparison functions and the property of the $ \rho _{\ast } $-admissibility play an important role. In the first step, the existence of fixed point theorems is proven for such a type of contractions in the context of the complete fuzzy metric spaces. Then, some of the results are extended in the framework of the fuzzy metric spaces equipped with a partial order. In this direction, we give some examples to clarify the obtained results and definitions. Additionally, we demonstrate an application about the solutions of non-linear matrix equations on the basis of fixed points of these new contractions.
- interpolative contraction,
- $ \rho _{\ast } $-admissible multivalued mapping,
- fuzzy metric space,
- partially ordered fuzzy metric space
Citation: Müzeyyen Sangurlu Sezen, Mohammed Jasim Mohammed, Sina Etemad, Jessada Tariboon. On the multivalued $ \rho _{\ast } $-interpolative contractions in fuzzy metric spaces with application to nonlinear matrix equations[J]. AIMS Mathematics, 2026, 11(2): 4263-4282. doi: 10.3934/math.2026171

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Abstract

In this study, the subject of the multivalued $ \rho _{\ast } $-interpolative Ćirić-Reich-Rus-type fuzzy contractions is introduced and investigated in which the $ \vartheta $-comparison functions and the property of the $ \rho _{\ast } $-admissibility play an important role. In the first step, the existence of fixed point theorems is proven for such a type of contractions in the context of the complete fuzzy metric spaces. Then, some of the results are extended in the framework of the fuzzy metric spaces equipped with a partial order. In this direction, we give some examples to clarify the obtained results and definitions. Additionally, we demonstrate an application about the solutions of non-linear matrix equations on the basis of fixed points of these new contractions.

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