IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v181y2024ics0960077924001401.html
   My bibliography  Save this article

Fractals of two types of enriched (q,θ)-Hutchinson–Barnsley operators

Author

Listed:
  • Anjum, Rizwan
  • Din, Muhammad
  • Zhou, Mi

Abstract

The aim of this paper is to introduce and develop two novel classifications of enriched (q,θ)-contractions on Banach spaces. The paper includes illustrative examples to demonstrate these concepts and establishes the convergence of Krasnoselskii’s iteration method when applied to approximate the fixed point of such enriched (q,θ)-contractions. Additionally, the paper explores the application of these concepts in constructing the fractals of the corresponding Hutchinson–Barnsley operators. The above construction is illustrated by some examples. These discoveries provide new fixed-point solutions for iterated function systems under various contractive conditions. Finally, as an application of our main result, the existence of the solution to the problem of fourth order differential equation is presented. Furthermore, the findings not only validate but also enhance and expand upon multiple established conclusions in the existing literature.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924001401
    DOI: 10.1016/j.chaos.2024.114589
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924001401
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.114589?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:eee:chsofr:v:181:y:2024:i:c:s0960077924001401. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.