Certain inequalities related with Hankel and Toeplitz determinant for q-starlike functions

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.