Hankel Determinant Estimates for Bi-Bazilevič-Type Functions Involving  q-Fibonacci Numbers

Authors

  • 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, Sultanate of Oman
  • Adel Salim Tayyah Department of Computer Science, College of Computer Science and Information Technology, University of Al-Qadisiyah, Diwaniyah, 58002 Iraq https://orcid.org/0000-0002-4380-1428
  • Ala Amourah Mathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 311, Oman
  • Abdullrahman A. Al-Maqbali Department of Basic and Applied Sciences, College of Applied and Health Sciences, A’Sharqiyah University, Post Box No. 42, Post Code No. 400, Ibra, Sultanate of Oman
  • Khaled Al Mashraf Department of Basic and Applied Sciences, College of Applied and Health Sciences, A’Sharqiyah University, Post Box No. 42, Post Code No. 400, Ibra, Sultanate of Oman
  • Tala Sasa Department of Mathematics, Faculty of Science, Applied Science Private University, Amman, Jordan

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6698

Keywords:

Analytic functions, Bi-univalent functions, Starlike class, Fekete–Szegö functional, Fibonacci sequence, \(\q\)-calculus, Shell-like curves

Abstract

 This study focuses on a specific class of analytic and bi-univalent functions of Bazilevič-type, formulated within a geometric context shaped by shell-like curves and influenced by the  q-analogue of Fibonacci numbers. By utilizing the subordination approach, we establish precise bounds for the initial coefficients in the Taylor–Maclaurin expansion of these functions. Moreover, the paper presents Fekete–Szegö-type inequalities and introduces novel bounds for the second Hankel determinant, thereby contributing to a deeper analytical insight into the behavior of this function class. These contributions not only broaden the scope of traditional coefficient problems related to bi-univalent functions but also highlight the intricate connections among geometric function theory, specialized function classes, and the principles of q-calculus. The outcomes pave the way for future studies aimed at deriving bounds for higher-order coefficients and examining determinant-related functionals under this theoretical model. 

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Published

2025-08-02

Issue

Vol. 18 No. 3: (July 2025)

Section

Mathematical Analysis

License

Copyright (c) 2025 Abdullah Alsoboh, Adel Salim Tayyah, Ala Amourah, Abdullrahman A. Al-Maqbali, Khaled Al Mashraf, Tala Sasa

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How to Cite

Hankel Determinant Estimates for Bi-Bazilevič-Type Functions Involving  q-Fibonacci Numbers. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6698. https://doi.org/10.29020/nybg.ejpam.v18i3.6698