Abstract
In the present article, we prove the sharp upper bounds for the second order Hankel determinants |H2(1)|, |H2(2)| and related functionals |a2a3 - a4|, |a2a5 - a3a4| for q-starlike functions. An upper bound for the third order Hankel determinant |H3(1)| along with the sharp upper bounds for Toeplitz determinant |Tm(n)|, where (m, n) ∈ {(2, 2), (2, 3), (3, 1), (3, 2)} are attained. Many known results are also obtained as corollaries of our main results.