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Czerwik Vector-Valued Metric Space with an Equivalence Relation and Extended Forms of Perov Fixed-Point Theorem

Author

Listed:
  • Monairah Alansari

    (Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Yahya Almalki

    (Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia)

  • Muhammad Usman Ali

    (Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, Islamabad 45550, Pakistan)

Abstract

In this article, we shall generalize the idea of vector-valued metric space and Perov fixed-point theorem. We shall introduce the notion of Czerwik vector-valued R -metric space by involving an equivalence relation. A few basic concepts and properties related to Czerwik vector-valued R -metric space shall also be discussed that are required to obtain a few extended types of Perov fixed-point theorem.

Suggested Citation

  • Monairah Alansari & Yahya Almalki & Muhammad Usman Ali, 2023. "Czerwik Vector-Valued Metric Space with an Equivalence Relation and Extended Forms of Perov Fixed-Point Theorem," Mathematics, MDPI, vol. 11(16), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3583-:d:1220319
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    References listed on IDEAS

    as
    1. Juan Martínez-Moreno & Dhananjay Gopal, 2021. "A Perov Version of Fuzzy Metric Spaces and Common Fixed Points for Compatible Mappings," Mathematics, MDPI, vol. 9(11), pages 1-14, June.
    2. Liliana Guran & Monica-Felicia Bota & Asim Naseem & Zoran D. Mitrović & Manuel de la Sen & Stojan Radenović, 2020. "On Some New Multivalued Results in the Metric Spaces of Perov’s Type," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
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