On Certain Classes of Bi-Bazilevic Functions Defined by q-Ruscheweyh Differential Operator

In this paper, we make use of the concept of fractional q-calculus to introduce two new classes of biBazilevic 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 a2 and a3 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.