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

Gunaseelan Mani ^[1] ; Balaji Ramalingam ^[1] ; Sina Etemad ^[3] ; Ibrahim Avcı ^[4] ; Shahram Rezapour ^[2]
1. [1] Saveetha University
  
  Saveetha University
  
  India
2. [2] China Medical University
  
  China Medical University
  
  Taiwán
3. [3] Azarbaijan Shahid Madani University & Al-Ayen University
4. [4] Final International University
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Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 3, 2024
Idioma: inglés
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Resumen
- 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