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Generalized α − ψ Rational‐Type Contractions and Related Fixed Point Results in Controlled Metric Spaces

Author

Listed:
  • Manoj Kumar
  • Swati Parashar
  • Pankaj Kumar
  • Rahul Shukla

Abstract

We introduce the new notion of generalized α − ψ rational type contractions of type I and type II in controlled metric spaces. By making use of these new notions, some fixed point theorems are also proved in the mentioned spaces for the α− admissible self maps. Some examples on the finite sets are also provided to prove the validity of our results. Some results which are direct consequences of the proved results are mentioned in the form of corollaries. As an application, an integral equation is solved with the aid of our results. Finally, a series electric circuit problem in the form of second‐order differential equation is solved by converting it into fixed point problem with the aid of the proved result.

Suggested Citation

  • Manoj Kumar & Swati Parashar & Pankaj Kumar & Rahul Shukla, 2025. "Generalized α − ψ Rational‐Type Contractions and Related Fixed Point Results in Controlled Metric Spaces," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:3878750
    DOI: 10.1155/jom/3878750
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    References listed on IDEAS

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    1. Sunil Beniwal & Naveen Mani & Rahul Shukla & Amit Sharma, 2024. "Fixed Point Results for Compatible Mappings in Extended Parametric S b -Metric Spaces," Mathematics, MDPI, vol. 12(10), pages 1-20, May.
    2. Nabil Mlaiki & Hassen Aydi & Nizar Souayah & Thabet Abdeljawad, 2018. "Controlled Metric Type Spaces and the Related Contraction Principle," Mathematics, MDPI, vol. 6(10), pages 1-7, October.
    3. Tayyab Kamran & Maria Samreen & Qurat UL Ain, 2017. "A Generalization of b -Metric Space and Some Fixed Point Theorems," Mathematics, MDPI, vol. 5(2), pages 1-7, March.
    4. Thabet Abdeljawad & Nabil Mlaiki & Hassen Aydi & Nizar Souayah, 2018. "Double Controlled Metric Type Spaces and Some Fixed Point Results," Mathematics, MDPI, vol. 6(12), pages 1-10, December.
    5. Muhib Abuloha & Doaa Rizk & Kamaleldin Abodayeh & Nabil Mlaiki & Thabet Abdeljawad & Naeem Saleem, 2021. "New Results in Controlled Metric Type Spaces," Journal of Mathematics, Hindawi, vol. 2021, pages 1-6, April.
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