Quantum Calculus Meets Toeplitz: Sharp Bounds for p-Valent Ma-Minda Classes

Abstract

In this paper, we investigate Toeplitz determinants associated with subclasses of p-valent q-starlike and q-convex Ma-Minda functions defined via the Jackson q-derivative operator. By employing subordination techniques together with coefficient estimates for functions having positive real part, we derive upper bounds for the Toeplitz determinants T_2 (p+1) and T_3 (p). In several cases, the obtained estimates are shown to be sharp through appropriate extremal functions. Our results unify and extend various earlier results available for classical univalent and multivalent function classes. Furthermore, by letting q→1^-, the corresponding results for the classical Ma-Minda starlike and convex classes are recovered as special cases. Applications to certain subclasses associated with Janowski, exponential, and cardioid-type domains are also discussed.