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On the Menger Probabilistic Bipolar Metric Spaces: Fixed Point Theorems and Applications

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Abstract

In this paper, we introduce a new class of metric spaces called the Menger probabilistic bipolar metric space and define some other notions related to this space. Moreover, we prove some uniqueness fixed point theorems for two cases including the covariant and contravariant maps. These fixed point theorems are new versions of the Banach contraction principle, Kannan theorem, and Reich-type theorem in the context of the Menger probabilistic bipolar metric space. Throughout the paper, we provide some examples to understand the definitions in the better manner. Finally, two applications are given for proving the uniqueness result in the form of an integral equation and a fractional boundary value problem.

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Acknowledgements

The third and fifth authors would like to thank Azarbaijan Shahid Madani University.

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Authors and Affiliations

  1. Department of Mathematics, Saveetha School of Engineering, Organization Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, Tamil Nadu, 602105, India

    Gunaseelan Mani & Balaji Ramalingam

  2. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

    Sina Etemad & Shahram Rezapour

  3. Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah, 64001, Iraq

    Sina Etemad

  4. Department of Computer Engineering, Faculty of Engineering, Final International University, Kyrenia, Northern Cyprus, Via Mersin 10, Turkey

    İbrahim Avcı

  5. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Shahram Rezapour

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  1. Gunaseelan Mani
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  2. Balaji Ramalingam
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  4. İbrahim Avcı
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  5. Shahram Rezapour
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The authors declare that the study was realized in collaboration with equal responsibility. All authors read and approved the final manuscript.

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Correspondence to Shahram Rezapour.

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Mani, G., Ramalingam, B., Etemad, S. et al. On the Menger Probabilistic Bipolar Metric Spaces: Fixed Point Theorems and Applications. Qual. Theory Dyn. Syst. 23, 99 (2024). https://doi.org/10.1007/s12346-024-00958-5

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  • DOI: https://doi.org/10.1007/s12346-024-00958-5

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