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An Extended b‐Metric‐Type Space and Related Fixed Point Theorems with an Application to Nonlinear Integral Equations

Author

Listed:
  • Kushal Roy
  • Sayantan Panja
  • Mantu Saha
  • Vahid Parvaneh

Abstract

In this paper, the concept of sequential p‐metric spaces has been introduced as a generalization of usual metric spaces, b‐metric spaces and specially of p‐metric spaces. Several topological properties of such spaces have been discussed here. In view of this notion, we prove fixed point theorems for some classes of contractive mappings over such spaces. Supporting examples have been given in order to examine the validity of the underlying space and in respect to our proven fixed point theorems.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:8868043
    DOI: 10.1155/2020/8868043
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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. 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.
    3. N. Mlaiki & K. Abodayeh & H. Aydi & T. Abdeljawad & M. Abuloha, 2018. "Rectangular Metric-Like Type Spaces and Related Fixed Points," Journal of Mathematics, Hindawi, vol. 2018, pages 1-7, September.
    4. 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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