IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i4p665-d754074.html
   My bibliography  Save this article

A New Best Proximity Point Result with an Application to Nonlinear Fredholm Integral Equations

Author

Listed:
  • Hakan Sahin

    (Department of Mathematics, Faculty of Science and Arts, Amasya University, Amasya 05000, Turkey)

Abstract

In the current paper, we first introduce a new class of contractions via a new notion called p -cyclic contraction mapping by combining the ideas of cyclic contraction mapping and p -contraction mapping. Then, we give a new definition of a cyclically 0-complete pair to weaken the completeness condition on the partial metric spaces. Following that, we prove some best proximity point results for p -cyclic contraction mappings on D ∪ E where D , E is a cyclically 0-complete pair in the setting of partial metric spaces. Hence, we generalize and unify famous and well-known results in the literature of metric fixed point theory. Additionally, we present some nontrivial examples to compare our results with earlier. Finally, we investigate the sufficient conditions for the existence of a solution to nonlinear Fredholm integral equations by the results in the paper.

Suggested Citation

  • Hakan Sahin, 2022. "A New Best Proximity Point Result with an Application to Nonlinear Fredholm Integral Equations," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:665-:d:754074
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/4/665/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/4/665/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Çetin Cemal Özeken & Cüneyt Çevik, 2021. "Ordered Vectorial Quasi and Almost Contractions on Ordered Vector Metric Spaces," Mathematics, MDPI, vol. 9(19), pages 1-8, October.
    2. Rafael Espínola & G. Sankara Raju Kosuru & P. Veeramani, 2015. "Pythagorean Property and Best-Proximity Point Theorems," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 534-550, February.
    Full references (including those not matched with items on IDEAS)

    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. Poom Kumam & Chirasak Mongkolkeha, 2019. "Global Optimization for Quasi-Noncyclic Relatively Nonexpansive Mappings with Application to Analytic Complex Functions," Mathematics, MDPI, vol. 7(1), pages 1-8, January.
    2. Slah Sahmim & Abdelbasset Felhi & Hassen Aydi, 2019. "Convergence and Best Proximity Points for Generalized Contraction Pairs," Mathematics, MDPI, vol. 7(2), pages 1-12, February.

    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:10:y:2022:i:4:p:665-:d:754074. 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.