Analytic Estimates for Bi-Univalent Functions Associated with a New Operator Involving the q–Rabotnov Function

Paper Details

Authors: Almalkawi A.; Amourah A.; Alsoboh A.; Salah J.; Al Mashrafi K.; Malkawi A.A.-R.; Sasa T.

DOI: 10.28924/2291-8639-24-2026-1

Journal: International Journal of Analysis and Applications

Year: 2026

Publisher: Etamaths Publishing

Document Type: Article

Open Access: All Open Access; Gold Open Access

Cited by: 5

Abstract

In this paper, we introduce and analyze a new subclass of bi-univalent functions associated with a differential operator constructed from the q–Rabotnov function. Motivated by the framework of q–calculus and its interplay with geometric function theory, the proposed operator is defined through convolution with q–Rabotnov kernels, thereby generating novel analytic structures. By applying the subordination principle, we establish sharp coefficient estimates for the initial Taylor–Maclaurin coefficients |α2 | and |α3 |, and derive Fekete–Szegö type inequalities for the class under consideration. The results presented here extend and generalize several recent contributions in the theory of bi-univalent functions, highlighting the central role of q–special functions in the development of new operator-based subclasses. These findings provide deeper insights into the analytic behavior of bi-univalent mappings and suggest further applications of q–calculus in operator theory, convolution structures, and complex analysis. © 2026 the author(s).

Keywords

analytic functions; Fekete–Szegö; Fibonacci numbers; q-Rabotnov func-tion; quantum calculus; univalent functions

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