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New Generalized Contractions by Employing Two Control Functions and Coupled Fixed-Point Theorems with Applications

Author

Listed:
  • Hasanen A. Hammad

    (Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi Arabia
    Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt)

  • Mohra Zayed

    (Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia)

Abstract

In this study, we obtain certain coupled fixed-point results for generalized contractions involving two control functions in a controlled metric space. Additionally, we establish some coupled fixed-point results in graph-enabled controlled metric spaces. Many well-known results from the literature will be expanded upon and modified by our results. In order to demonstrate the validity of the stated results, we also offer some examples. Finally, we apply the theoretical results to obtain the solution to a system of integral equations.

Suggested Citation

  • Hasanen A. Hammad & Mohra Zayed, 2022. "New Generalized Contractions by Employing Two Control Functions and Coupled Fixed-Point Theorems with Applications," Mathematics, MDPI, vol. 10(17), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3208-:d:907152
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    References listed on IDEAS

    as
    1. Hasanen A. Hammad & Praveen Agarwal & Juan L. G. Guirao, 2021. "Applications to Boundary Value Problems and Homotopy Theory via Tripled Fixed Point Techniques in Partially Metric Spaces," Mathematics, MDPI, vol. 9(16), pages 1-22, August.
    2. 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.
    3. Hasanen A. Hammad & Hassen Aydi & Manuel De la Sen & Atila Bueno, 2021. "Solutions of Fractional Differential Type Equations by Fixed Point Techniques for Multivalued Contractions," Complexity, Hindawi, vol. 2021, pages 1-13, February.
    4. 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.
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