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A New Variant of Symmetric Distance Spaces and an Extension of the Banach Fixed‐Point Theorem

Author

Listed:
  • Kushal Roy
  • Mantu Saha
  • Vahid Parvaneh
  • Maryam Khorshidi

Abstract

The notion of Δ‐metric spaces has been proposed in this study as a generalization of b‐metric spaces, extended b‐metric spaces, and p‐metric spaces. A number of topological characteristics of such spaces have been investigated in this paper. On such spaces, a noncompactness measure has been established, and some results in the framework of noncompactness measure have been achieved. We prove an analogous of the Banach contraction principle in such spaces based on this approach. In order to investigate the validity of the underlying space and our proven fixed‐point theorems, supporting examples have been presented. Furthermore, the well‐posedness of the fixed‐point problem has been tested using our fixed‐point result.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:9282762
    DOI: 10.1155/2022/9282762
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    References listed on IDEAS

    as
    1. 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.
    2. Józef Banaś & Mohammad Mursaleen, 2014. "Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations," Springer Books, Springer, edition 127, number 978-81-322-1886-9, January.
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