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

Abdullah Alsoboh (), Ala Amourah (), Omar Alnajar, Mamoon Ahmed and Tamer M. Seoudy
Additional contact information
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
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

Mathematics, 2025, vol. 13, issue 8, 1-14

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.

Keywords: analytic functions; univalent functions; star-like functions; Fibonacci numbers; Fibonacci polynomials; shell-like curves; quantum calculus (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/8/1294/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/8/1294/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:8:p:1294-:d:1635259

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().