IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i1p238-d1023338.html
   My bibliography  Save this article

Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation

Author

Listed:
  • Fahim Ud Din

    (Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan)

  • Muhammad Din

    (Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan)

  • Umar Ishtiaq

    (Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54782, Pakistan)

  • Salvatore Sessa

    (Dipartimento di Architettura, Università Dinapoli Federico II, Via Toledo 403, 80121 Napoli, Italy)

Abstract

The purpose of this article is to discuss some new aspects of the vector-valued metric space. The idea of an arbitrary binary relation along with the well-known F contraction is used to demonstrate the existence of fixed points in the context of a complete vector-valued metric space for both single- and multi-valued mappings. Utilizing the idea of binary relation, and with the help of F contraction, this work extends and complements some of the very recently established Perov-type fixed-point results in the literature. Furthermore, this work includes examples to justify the validity of the given results. During the discussion, it was found that some of the renowned metrical results proven by several authors using different binary relations, such as partial order, pre-order, transitive relation, tolerance, strict order and symmetric closure, can be weakened by using an arbitrary binary relation.

Suggested Citation

  • Fahim Ud Din & Muhammad Din & Umar Ishtiaq & Salvatore Sessa, 2023. "Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation," Mathematics, MDPI, vol. 11(1), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:1:p:238-:d:1023338
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/1/238/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/1/238/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ishak Altun & Nawab Hussain & Muhammad Qasim & Hamed H. Al-Sulami, 2019. "A New Fixed Point Result of Perov Type and Its Application to a Semilinear Operator System," Mathematics, MDPI, vol. 7(11), pages 1-10, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Anjum, Rizwan & Din, Muhammad & Zhou, Mi, 2024. "Fractals of two types of enriched (q,θ)-Hutchinson–Barnsley operators," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wei-Shih Du & Chung-Chuan Chen & Marko Kostić & Bessem Samet, 2023. "Preface to the Special Issue “Fixed Point Theory and Dynamical Systems with Applications”," Mathematics, MDPI, vol. 11(13), pages 1-2, June.
    2. Jamshaid Ahmad & Saleh Abdullah Al-Mezel & Ravi P. Agarwal, 2022. "Fixed Point Results for Perov–Ćirić–Prešić-Type Θ-Contractions with Applications," Mathematics, MDPI, vol. 10(12), pages 1-11, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:1:p:238-:d:1023338. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.