This research paper focuses on obtaining sharp bounds for Toeplitz determinants whose entries are the coefficients of starlike functions satisfying specific conditions. The conditions are related to the quantity zDqf(z)f(z), which is required to lie in a specific subset of the right half-plane. The study presents new special cases and known results in this context. The research approach involves using Toeplitz determinants and their properties, and the results are obtained through a combination of mathematical techniques, including q-calculus.

Keywords: Univalent functions, Subordination, Toeplitz determinants, Fekete-Szegȍ inequality, q-Calculus