Abstract:

In this paper, we introduce a symmetric balloon-shaped domain generated by a q-analytic mapping and defines a Ma--Minda type subclass of bi-univalent functions via subordination. The role of q-calculus in controlling the domain geometry is highlighted. Sharp bounds for the coefficients |\vartheta_2| and |\vartheta_3| are obtained using q-integers, together with a piecewise estimate for the Fekete-Szego functional |\vartheta_3-\lambda\vartheta_2^2|. Growth, distortion, and the limiting case q \to 1^{-} are discussed, recovering classical results.