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Double Controlled Metric Type Spaces and Some Fixed Point Results

Author

Listed:
  • Thabet Abdeljawad

    (Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia)

  • Nabil Mlaiki

    (Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia)

  • Hassen Aydi

    (Department of Mathematics, College of Education in Jubail, Imam Abdulrahman Bin Faisal University, P.O. Box 12020, Jubail 31961, Saudi Arabia)

  • Nizar Souayah

    (Department of Natural Sciences, Community College Al-Riyadh, King Saud University, Riyadh 4545, Saudi Arabia)

Abstract

In this article, in the sequel of extending b -metric spaces, we modify controlled metric type spaces via two control functions α ( x , y ) and μ ( x , y ) on the right-hand side of the b - triangle inequality, that is, d ( x , y ) ≤ α ( x , z ) d ( x , z ) + μ ( z , y ) d ( z , y ) , for all x , y , z ∈ X . Some examples of a double controlled metric type space by two incomparable functions, which is not a controlled metric type by one of the given functions, are presented. We also provide some fixed point results involving Banach type, Kannan type and ϕ -nonlinear type contractions in the setting of double controlled metric type spaces.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:320-:d:189937
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    Citations

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    Cited by:

    1. Jia Deng & Xiaolan Liu & Yan Sun & Mi Zhou, 2022. "Fixed Point Results for a New Rational Contraction in Double Controlled Metric-like Spaces," Mathematics, MDPI, vol. 10(9), pages 1-12, April.
    2. Naeem Saleem & Salman Furqan & Kinda Abuasbeh & Muath Awadalla, 2023. "Fuzzy Triple Controlled Metric like Spaces with Applications," Mathematics, MDPI, vol. 11(6), pages 1-30, March.
    3. 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.
    4. 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.

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