IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v6y2018i11p221-d178834.html
   My bibliography  Save this article

Best Proximity Point Results in b -Metric Space and Application to Nonlinear Fractional Differential Equation

Author

Listed:
  • Azhar Hussain

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

  • Tanzeela Kanwal

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

  • Muhammad Adeel

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

  • Stojan Radenovic

    (Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia)

Abstract

Based on the concepts of contractive conditions due to Suzuki (Suzuki, T., A generalized Banach contraction principle that characterizes metric completeness, Proceedings of the American Mathematical Society, 2008, 136, 1861–1869) and Jleli (Jleli, M., Samet, B., A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014, 2014, 38), our aim is to combine the aforementioned concepts in more general way for set valued and single valued mappings and to prove the existence of best proximity point results in the context of b -metric spaces. Endowing the concept of graph with b -metric space, we present some best proximity point results. Some concrete examples are presented to illustrate the obtained results. Moreover, we prove the existence of the solution of nonlinear fractional differential equation involving Caputo derivative. Presented results not only unify but also generalize several existing results on the topic in the corresponding literature.

Suggested Citation

  • Azhar Hussain & Tanzeela Kanwal & Muhammad Adeel & Stojan Radenovic, 2018. "Best Proximity Point Results in b -Metric Space and Application to Nonlinear Fractional Differential Equation," Mathematics, MDPI, vol. 6(11), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:11:p:221-:d:178834
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/6/11/221/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/6/11/221/
    Download Restriction: no
    ---><---

    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:221-:d:178834. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.