IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i21p4138-d964577.html
   My bibliography  Save this article

Existence and Approximation of Fixed Points of Enriched φ -Contractions in Banach Spaces

Author

Listed:
  • Vasile Berinde

    (Department of Mathematics and Computer Science, Technical University of Baia Mare, North University Center at Baia Mare, 430122 Baia Mare, Romania
    Academy of Romanian Scientists, 010071 Bucharest, Romania)

  • Jackie Harjani

    (Department of Mathematics, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain)

  • Kishin Sadarangani

    (Department of Mathematics, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain)

Abstract

We introduce the class of enriched φ -contractions in Banach spaces as a natural generalization of φ -contractions and study the existence and approximation of the fixed points of mappings in this new class, which is shown to be an unsaturated class of mappings in the setting of a Banach space. We illustrated the usefulness of our fixed point results by studying the existence and uniqueness of the solutions of some second order ( p , q ) -difference equations with integral boundary value conditions.

Suggested Citation

  • Vasile Berinde & Jackie Harjani & Kishin Sadarangani, 2022. "Existence and Approximation of Fixed Points of Enriched φ -Contractions in Banach Spaces," Mathematics, MDPI, vol. 10(21), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4138-:d:964577
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/21/4138/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/21/4138/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. V. Berinde & A. Petruşel & I. A. Rus & M. A. Şerban, 2016. "The Retraction-Displacement Condition in the Theory of Fixed Point Equation with a Convergent Iterative Algorithm," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Vijay Gupta (ed.), Mathematical Analysis, Approximation Theory and Their Applications, pages 75-106, Springer.
    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. Claudia Luminiţa Mihiţ & Ghiocel Moţ & Gabriela Petruşel, 2022. "Ćirić-Type Operators and Common Fixed Point Theorems," Mathematics, MDPI, vol. 10(11), pages 1-9, 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:10:y:2022:i:21:p:4138-:d:964577. 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.