Sharp Estimates for q-Convex Functions and the Associated Classical Family

In this article, we introduce and study two new subclasses of analytic univalent functions defined via the Ma–Minda function. Specifically, we consider the class Cξq of q-convex functions involving a suitable Ma–Minda function ξq(z), together with its classical counterpart Cξ corresponding to ξ(z), where 0<q<1. We determine bounds for the first few Taylor–Maclaurin coefficients and deduce Fekete–Szegö and Kruskal inequality. Moreover, we obtain the associated Toeplitz determinants related to this class. We highlight several new consequences of our results that are of independent interest in geometric function theory.