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Solving Periodic Boundary Value Problem via Product Type Rational Contractions

Author

Listed:
  • Saif Ur Rehman
  • Abeeda Ahmad
  • Mohammed M. M. Jaradat
  • Sidra Akbar
  • Aneeza Hafeez
  • Faiz Ullah
  • Nawab Hussain

Abstract

In this paper, we define some new product types of rational contractions for single-valued mappings in generalized metric spaces. We prove the uniqueness of fixed point (FP) and common fixed point (CFP) theorems under the new product types of rational contractions in generalized metric spaces with the application of boundary value problem. In support of our results, we present nontrivial illustrative examples for the uniqueness of FP and CFP in generalized metric spaces. Furthermore, we present an application of the first-order periodic boundary value problem for the existence of unique solutions to unify our work. Using this approach, one can prove some more attractive unique FP and CFP results for different types of modified rational contractions in generalized metric spaces with the application of integral equations and boundary value problems.

Suggested Citation

  • Saif Ur Rehman & Abeeda Ahmad & Mohammed M. M. Jaradat & Sidra Akbar & Aneeza Hafeez & Faiz Ullah & Nawab Hussain, 2024. "Solving Periodic Boundary Value Problem via Product Type Rational Contractions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2024, pages 1-22, December.
    • Handle: RePEc:hin:jijmms:9978064
    DOI: 10.1155/2024/9978064
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