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A Generalization of b -Metric Space and Some Fixed Point Theorems

Author

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  • Tayyab Kamran

    (Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
    Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad 44000, Pakistan)

  • Maria Samreen

    (Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan)

  • Qurat UL Ain

    (Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan)

Abstract

In this paper, inspired by the concept of b -metric space, we introduce the concept of extended b -metric space. We also establish some fixed point theorems for self-mappings defined on such spaces. Our results extend/generalize many pre-existing results in literature.

Suggested Citation

  • Tayyab Kamran & Maria Samreen & Qurat UL Ain, 2017. "A Generalization of b -Metric Space and Some Fixed Point Theorems," Mathematics, MDPI, vol. 5(2), pages 1-7, March.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:2:p:19-:d:93907
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    References listed on IDEAS

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    1. Maria Samreen & Tayyab Kamran & Naseer Shahzad, 2013. "Some Fixed Point Theorems in -Metric Space Endowed with Graph," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, October.
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    Cited by:

    1. Kushal Roy & Mantu Saha & Vahid Parvaneh & Maryam Khorshidi, 2022. "A New Variant of Symmetric Distance Spaces and an Extension of the Banach Fixed‐Point Theorem," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    2. Manoj Kumar & Swati Parashar & Pankaj Kumar & Rahul Shukla, 2025. "Generalized α − ψ Rational‐Type Contractions and Related Fixed Point Results in Controlled Metric Spaces," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    3. Surjeet Singh Chauhan (Gonder) & Prachi Garg & Kamleshwar Thakur, 2022. "Study of Metric Space and Its Variants," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    4. Shivani Kukreti & Shivam Rawat & Mohammad Sajid & R. C. Dimri, 2025. "Fixed‐Point Result for Generalized Enriched Contractions With Applications in Cantilever Beam Problem and Homotopy Theory," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    5. Jayashree Patil & Basel Hardan & Ahmed A. Hamoud & Amol Bachhav & Homan Emadifar & Afshin Ghanizadeh & Seyyed Ahmad Edalatpanah & Hooshmand Azizi, 2022. "On (η, γ)(f, g)‐Contractions in Extended b‐Metric Spaces," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    6. Quanita Kiran & Mamuna Azhar & Hassen Aydi & Yaé Ulrich Gaba, 2021. "Admissible Hybrid Z‐Contractions in Extended b‐Metric Spaces," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    7. Azham Ilyass & Naveen Mani & Rahul Shukla, 2025. "Reich Graph Contraction in Graphically Extended b‐Metric Spaces With Applications to Cantilever Beam Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    8. Kushal Roy & Sayantan Panja & Mantu Saha & Vahid Parvaneh, 2020. "An Extended b‐Metric‐Type Space and Related Fixed Point Theorems with an Application to Nonlinear Integral Equations," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    9. Amiri, Pari & Afshari, Hojjat, 2022. "Common fixed point results for multi-valued mappings in complex-valued double controlled metric spaces and their applications to the existence of solution of fractional integral inclusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    10. Swati Parashar & Manoj Kumar & Pankaj Kumar & Rahul Shukla, 2025. "Controlled Metric Space and Fixed Point Theorems for Jaggi–Suzuki–Type Hybrid Contraction," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    11. Shengquan Weng & Hongying Xiao, 2025. "Related Fixed Point Results for LB3S2‐Type Cyclic Mapping in Extended b‐Metric Spaces With an Application," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    12. Umar Ishtiaq & Salha Alshaikey & Muhammad Bilal Riaz & Khaleel Ahmad, 2024. "Fixed point results in intuitionistic fuzzy pentagonal controlled metric spaces with applications to dynamic market equilibrium and satellite web coupling," PLOS ONE, Public Library of Science, vol. 19(8), pages 1-33, August.

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    1. Azham Ilyass & Naveen Mani & Rahul Shukla, 2025. "Reich Graph Contraction in Graphically Extended b‐Metric Spaces With Applications to Cantilever Beam Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).

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