A Study of Bi-Univalent Class in Leaf-Like Domains Using Quantum Calculus Through Subordination

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DOI: https://doi.org/10.28924/2291-8639-23-2025-293
Published: Nov 13, 2025
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Abdullah Alsoboh, Ala Amourah, Waggas Galib Atshan, Jamal Salah, Tala Sasa, A Study of Bi-Univalent Class in Leaf-Like Domains Using Quantum Calculus Through Subordination, Int. J. Anal. Appl., 23 (2025), 293.

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Abdullah Alsoboh, Ala Amourah, Waggas Galib Atshan, Jamal Salah, Tala Sasa

Abstract

In this work, we introduce and study a new subclass of bi-univalent analytic functions that are associated with a leaf-shaped region, formulated through the framework of q-calculus and the principle of subordination. employing appropriate analytical techniques, we derive sharp coefficient estimates with a particular focus on the initial bounds for |a2| and |a3|, which play a central role in geometric function theory. In addition, we establish Fekete–Szegö-type inequalities for functions belonging to the proposed class, thereby extending and complementing several existing results in the literature. To illustrate the theoretical findings, we provide explicit examples and graphical representations that highlight the behavior of functions in the class under consideration. The analysis not only broadens the applicability of q-calculus methods in the study of bi-univalent functions but also contributes to a deeper understanding of function classes connected with geometrically significant domains. Potential avenues for further research and connections to related subclasses are also discussed.

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