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Functional Contractions Depending on a Pair of Test Functions Under Locally Transitive Binary Relations With Applications to Nonlinear Integral Equations

Author

Listed:
  • Doaa Filali
  • Faizan Ahmad Khan
  • Maha F. Alsharari
  • Shurooq Bader Alblawie
  • Mona Yahya Alfefi
  • Esmail Alshaban

Abstract

This study explores certain discoveries regarding fixed points under a functional contraction incorporating two test functions within the setup of a metric space equipped with a locally transitive relation. The outcomes investigated herewith refined, expanded, and strengthened several previously established fixed‐point findings. We provide numerous illustrative instances that demonstrated the credibility of our findings. We investigate the existence and uniqueness of solutions to specific nonlinear integral equations in order to ensure the practical use of our findings.

Suggested Citation

  • Doaa Filali & Faizan Ahmad Khan & Maha F. Alsharari & Shurooq Bader Alblawie & Mona Yahya Alfefi & Esmail Alshaban, 2025. "Functional Contractions Depending on a Pair of Test Functions Under Locally Transitive Binary Relations With Applications to Nonlinear Integral Equations," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:9003182
    DOI: 10.1155/jom/9003182
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    References listed on IDEAS

    as
    1. Doaa Filali & Faizan Ahmad Khan, 2024. "Suzuki–Ćirić-Type Nonlinear Contractions Employing a Locally ζ -Transitive Binary Relation with Applications to Boundary Value Problems," Mathematics, MDPI, vol. 12(13), pages 1-12, June.
    2. Nidal H. E. Eljaneid & Faizan A. Khan & Hamid I. A. Mohammed & Aftab Alam, 2022. "Relational Quasicontractions and Related Fixed Point Theorems," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    3. Khursheed J. Ansari & Salvatore Sessa & Aftab Alam, 2023. "A Class of Relational Functional Contractions with Applications to Nonlinear Integral Equations," Mathematics, MDPI, vol. 11(15), pages 1-11, August.
    4. Tahair Rasham & Giuseppe Marino & Abdullah Shoaib, 2019. "Fixed Points for a Pair of F -Dominated Contractive Mappings in Rectangular b -Metric Spaces with Graph," Mathematics, MDPI, vol. 7(10), pages 1-9, September.
    5. Faizan Ahmad Khan & Fahad M. Alamrani & Esmail Alshaban & Ebrahem A. Algehyne & Musaad S. Aldhabani & Dengfeng Lu, 2024. "Relation-Theoretic Contractions Employing a New Pair of Shifting Distance Functions with Applications to Second-Order Ordinary Differential Equations," Journal of Mathematics, Hindawi, vol. 2024, pages 1-9, October.
    6. Tahair Rasham & Abdullah Shoaib & Badriah A. S. Alamri & Muhammad Arshad, 2018. "Fixed Point Results for Multivalued Contractive Mappings Endowed with Graphic Structure," Journal of Mathematics, Hindawi, vol. 2018, pages 1-8, December.
    7. Nidal H. E. Eljaneid & Faizan A. Khan & Hamid I. A. Mohammed & Aftab Alam & Sumit Chandok, 2022. "Relational Quasicontractions and Related Fixed Point Theorems," Journal of Mathematics, Hindawi, vol. 2022, pages 1-6, August.
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