IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i8p1294-d1635259.html
   My bibliography  Save this article

Exploring q -Fibonacci Numbers in Geometric Function Theory: Univalence and Shell-like Starlike Curves

Author

Listed:
  • Abdullah Alsoboh

    (Department of Basic and Applied Sciences, College of Applied and Health Sciences, A’Sharqiyah University, Post Box No. 42, Post Code No. 400, Ibra 413, Oman)

  • Ala Amourah

    (Mathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 311, Oman
    Applied Science Research Center, Applied Science Private University, Amman 11941, Jordan)

  • Omar Alnajar

    (Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia)

  • Mamoon Ahmed

    (Department of Basic Sciences, Princess Sumaya University for Technology, Amman 11941, Jordan)

  • Tamer M. Seoudy

    (Department of Mathematics, Jamoum University College, Umm Al-Qura University, Makkah 21955, Saudi Arabia)

Abstract

Emphasising their connection with shell-like star-like curves, this work investigates a new subclass of star-like functions defined by q -Fibonacci numbers and q -polynomials. We study the geometric and analytic properties of this subclass, including the computation of intervals of univalence and nonunivalence for some functions. Moreover, we define a sufficient condition for functions in this subclass to satisfy the criteria of the famous class of analytic functions with positive real components. This work improves our understanding of the link between Fibonacci-type sequences and the geometric properties of analytic functions by using subordination ideas and the features of q -Fibonacci sequences. Emphasising the possibility for diverse research in combinatorial and analytical mathematics, the results offer fresh insights and support further study on the applications of calculus in geometric function theory.

Suggested Citation

  • Abdullah Alsoboh & Ala Amourah & Omar Alnajar & Mamoon Ahmed & Tamer M. Seoudy, 2025. "Exploring q -Fibonacci Numbers in Geometric Function Theory: Univalence and Shell-like Starlike Curves," Mathematics, MDPI, vol. 13(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1294-:d:1635259
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/8/1294/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/8/1294/
    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:13:y:2025:i:8:p:1294-:d:1635259. 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.