$q$--Rabotnov Functions and Bi-univalent Functions

Authors

  • Abdullah Alsoboh College of Applied and Health Sciences, ASharqiyah University, Post Box No. 42,\\ Post Code No. 400, Ibra, Sultanate of Oman
  • Ala Amourah Department of Mathematics, Faculty of Education and Arts, Sohar University, Sohar 3111, Sultanate of Oman,
  • Omar Alnajar Department of Mathematical Sciences, Faculty of Science and Technology, \\ Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia
  • Fahad Al Abri adara University Research Center, Jadara University, Jordan
  • Tala Sasa Department of Mathematics, Faculty of Science, Applied Science Private University, Amman, Jordan

DOI:

https://doi.org/10.29020/nybg.ejpam.v19i1.7109

Keywords:

Subordination, ultraspherical Polynomial, $\q$-Calculus, analytic functions,, univalent functions, bi-univalent functions, orthogonal polynomials, carathéodory's functions, fekete-Szeg\"{o} problem

Abstract

In this work, we introduce and investigate a new subclass of bi-univalent functions, denoted by $\mathfrak{R}_{\Sigma}^{\mu,x}(\varrho,\varphi,\lambda;\gamma;q)$, which is defined through the interplay between $q$--Rabotnov functions and $q$--Gegenbauer polynomials. For functions in this class, we derive sharp bounds for the initial Taylor--Maclaurin coefficients $|a_{2}|$ and $|a_{3}|$, and we establish estimates for the corresponding Fekete--Szeg\H{o} functional. Furthermore, by selecting suitable parameter values, our results reduce to several well known subclasses, thereby yielding a range of new consequences and extensions in the theory of analytic bi-univalent functions.

References

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Published

2026-02-22

Issue

Vol. 19 No. 1: (January 2026)

Section

Complex Analysis

License

Copyright (c) 2026 Abdullah Alsoboh, Ala Amourah, Omar Alnajar, Fahad Al Abri, Tala Sasa

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How to Cite

$q$--Rabotnov Functions and Bi-univalent Functions. (2026). European Journal of Pure and Applied Mathematics, 19(1), 7109. https://doi.org/10.29020/nybg.ejpam.v19i1.7109