IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v6y2018i11p256-d183494.html
   My bibliography  Save this article

Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces

Author

Listed:
  • Erdal Karapinar

    (Department of Mathematics, Atilim University, Incek 06836, Ankara, Turkey
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Ravi Agarwal

    (Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA)

  • Hassen Aydi

    (College of Education in Jubail, Department of Mathematics, Imam Abdulrahman Bin Faisal University, P.O. 12020, Industrial Jubail 31961, Saudi Arabia)

Abstract

By giving a counter-example, we point out a gap in the paper by Karapinar (Adv. Theory Nonlinear Anal. Its Appl. 2018, 2, 85–87) where the given fixed point may be not unique and we present the corrected version. We also state the celebrated fixed point theorem of Reich–Rus–Ćirić in the framework of complete partial metric spaces, by taking the interpolation theory into account. Some examples are provided where the main result in papers by Reich (Can. Math. Bull. 1971, 14, 121–124; Boll. Unione Mat. Ital. 1972, 4, 26–42 and Boll. Unione Mat. Ital. 1971, 4, 1–11.) is not applicable.

Suggested Citation

  • Erdal Karapinar & Ravi Agarwal & Hassen Aydi, 2018. "Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces," Mathematics, MDPI, vol. 6(11), pages 1-7, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:11:p:256-:d:183494
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/6/11/256/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/6/11/256/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hassen Aydi & Sana Hadj Amor & Erdal Karapınar, 2013. "Berinde-Type Generalized Contractions on Partial Metric Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, February.
    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. Erdal Karapınar & Ravi P. Agarwal & Seher Sultan Yeşilkaya & Chao Wang, 2022. "Fixed-Point Results for Meir–Keeler Type Contractions in Partial Metric Spaces: A Survey," Mathematics, MDPI, vol. 10(17), pages 1-76, August.
    2. Prithvi, B.V. & Katiyar, S.K., 2022. "Interpolative operators: Fractal to multivalued fractal," Chaos, Solitons & Fractals, Elsevier, vol. 164(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.

      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:6:y:2018:i:11:p:256-:d:183494. 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.