Bounds on Hankel Determinants with Fekete-Szegö Parameter for Bazilević Functions

<ns7:p>This paper presents a systematic investigation of a newly defined comprehensive subclass of analytic and univalent functions in the open unit disk. The introduced function class constitutes a broad generalization that incorporates several significant families, particularly Yamaguchi functions and starlike functions, which themselves exhibit fundamental properties within the established Bazilevič function hierarchy. The formal construction of this class employs the Ma-Minda framework through the application of subordination principles, set-theoretic operations, and analytical formulations involving infinite series and product combinations of specific geometric expressions. The principal contributions of this work include the derivation of sharp coefficient bounds, complete solutions for the Fekete-Szegö problem with parameters, and precise estimates for Hankel determinants containing a real parameter. The proposed class demonstrates remarkable generality, as it systematically reduces to numerous well-established function classes when its parameters are specialized to particular values within their defined domains, thereby providing a unified approach to studying these classical families.</ns7:p>