Proceedings of International Conference on Applied Innovation in IT  ·  2026/06/12  ·  Vol. 14  ·  Issue 4  ·  pp. 399–406
Quasi-Subordination on Bi-Univalent Functions Involving a Generalized Operator Associated with Horadam Polynomials
Mustafa H. Abd Ali and Mohammed H. Saloomi
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Abstract
Although numerous subclasses of bi-univalent functions have been investigated in recent years, coefficient estimates associated with generalized Q-operators and Horadam polynomials remain comparatively unexplored. Motivated by this gap, in this paper, we introduce and investigate a new subclass of the class Σ of analytic and bi-univalent functions defined in the open unit disk. The proposed subclass is constructed by means of the operator χ_(q,t)^(ƛ,ξ) in association with the Horadam polynomials h_n (x), which play an important role in various areas of mathematical analysis. By employing this operator, we establish a novel framework that enables us to study the geometric properties of functions belonging to this subclass. In particular, we derive estimates for the initial Taylor–Maclaurin coefficients for functions in the considered class. These coefficient bounds contribute to the ongoing development of coefficient problems in the theory of bi-univalent functions. Furthermore, several known results are obtained as special cases of our main findings by suitably specializing the parameters involved. The results presented in this work not only generalize earlier studies but also provide new insights and potential directions for future research in this field.
Keywords
Bi-Univalent Functions Functions Hadamard Product Holomorphic Function Horadam Polynomials Hurwitz-Lerch Zeta Quasi-Subordination Q-Srivastava-Attiya Operator Subordination
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