IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i22p3531-d1519322.html
   My bibliography  Save this article

A Generalised Difference Equation and Its Dynamics and Solutions

Author

Listed:
  • Ramazan Karatas

    (Education Faculty, Akdeniz University, Antalya 07058, Turkey
    These authors contributed equally to this work.)

  • Ali Gelişken

    (Faculty of Engineering and Natural Sciences, Konya Technical University, Konya 42250, Turkey
    These authors contributed equally to this work.)

  • Murat Arı

    (Faculty of Sciences, Karamanoğlu Mehmetbey University, Karaman 70200, Turkey
    These authors contributed equally to this work.)

Abstract

Rational difference equations have a wide range of applications in various fields of science. To illustrate, the equation x n + 1 = a + b x n c + d x n , n = 0 , 1 , . . . , known as the Riccati difference equation, has been applied in the field of optics. In this study, the global asymptotic stability of the difference equation x n + 1 = A x n − 2 k + j + 1 B + C x n − ( k + j ) x n − 2 k + j + 1 , n = 0 , 1 , . . . , is proved. The solutions of this difference equation are obtained by applying the standard iteration method, and the periodicity of these solutions is determined. Furthermore, this difference equation represents a generalisation of the results obtained in previous studies.

Suggested Citation

  • Ramazan Karatas & Ali Gelişken & Murat Arı, 2024. "A Generalised Difference Equation and Its Dynamics and Solutions," Mathematics, MDPI, vol. 12(22), pages 1-9, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3531-:d:1519322
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/22/3531/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/22/3531/
    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:12:y:2024:i:22:p:3531-:d:1519322. 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.