WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
On Certain Classes of Bi-Bazilevic Functions Defined by q-Ruscheweyh Differential Operator
Author:
Abstract: In this paper, we make use of the concept of fractional $$q$$-calculus to introduce two new classes of bi-
Bazilevic functions involving q-Ruscheweyh differential operator that are subordinate to Gegenbauer polynomials
and q-analogue of hyperbolic tangent functions. This study explores the characteristics and behaviors of these
functions, offering estimates for the modulus of the initial Taylor series coefficients $$a_{2}$$ and $$a_{3}$$ within this specific
class and their various subclasses. Additionally, this study delves into the classical Fekete-Szeg¨o functional problem
concerning functions $$f$$ that are part of our newly defined class and several of their subclasses.
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Keywords: Bi-Univalent Functions, Bi-Bazilevic, $$q$$-Ruscheweyh Differential Operator, Jackson $$q$$-Derivative
Operator, $$q$$-Gamma Function, Fractional $$q$$-Calculus Operator, Gegenbauer Polynomials, $$q$$-analogue of Hyperbolic
Tangent Functions, Coefficient Estimates, Fekete-Szeg¨o Functional Problem, Convolution, Hadamard Product
Pages: 144-156
DOI: 10.37394/23206.2025.24.15