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Fixed Point Results in Controlled Metric Spaces with Applications

Author

Listed:
  • Abdullah Eqal Al-Mazrooei

    (Department of Mathematics, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia)

  • Jamshaid Ahmad

    (Department of Mathematics, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia)

Abstract

The aim of this paper is to obtain some common fixed point theorems for generalized contractions involving certain control functions in controlled metric space and derive some generalized fixed point results as a consequence of our main results. We also prove some common fixed point theorems in controlled metric spaces endowed with a graph. Our results will generalize and amend many famous results from the literature. We also provide an example to show the authenticity of the established results. As an application of our main result, we investigate the solution of integral equations.

Suggested Citation

  • Abdullah Eqal Al-Mazrooei & Jamshaid Ahmad, 2022. "Fixed Point Results in Controlled Metric Spaces with Applications," Mathematics, MDPI, vol. 10(3), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:490-:d:741271
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    References listed on IDEAS

    as
    1. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

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