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A New Extension of the Rectangular b‐Metric Spaces

Author

Listed:
  • Nabil Mlaiki
  • Mohamed Hajji
  • Thabet Abdeljawad

Abstract

In this paper, we introduce a generalization of rectangular b‐metric spaces, by changing the rectangular inequality as follows: Dζ(a, b) ≤ ζ(a, b, u, v)[Dζ(a, u) + Dζ(u, v) + Dζ(v, b)], for all distinct a, b, u, v ∈ X. We prove some fixed point theorems, and we use our results to present a nice application in the last section of this paper.

Suggested Citation

  • Nabil Mlaiki & Mohamed Hajji & Thabet Abdeljawad, 2020. "A New Extension of the Rectangular b‐Metric Spaces," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:8319584
    DOI: 10.1155/2020/8319584
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    References listed on IDEAS

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    1. Hui-Sheng Ding & Zoran Kadelburg & Erdal Karapınar & Stojan Radenović, 2012. "Common Fixed Points of Weak Contractions in Cone Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. 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.
    3. Hui-Sheng Ding & Zoran Kadelburg & Erdal Karapınar & Stojan Radenović, 2012. "Common Fixed Points of Weak Contractions in Cone Metric Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-18, May.
    4. Haitham Qawaqneh & Mohd Salmi Md Noorani & Wasfi Shatanawi & Hassen Aydi & Habes Alsamir, 2019. "Fixed Point Results for Multi-Valued Contractions in b −Metric Spaces and an Application," Mathematics, MDPI, vol. 7(2), pages 1-13, February.
    5. 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.
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