Hankel, Toeplitz, and Hermitian-Toeplitz Determinants for Certain Close-to-convex Functions

Let f be analytic in D = { z ∈ C : | z | < 1 } , and be given by f ( z ) = z + ∑ n = 2 ∞ a n z n . We give sharp bounds for the second Hankel determinant, some Toeplitz, and some Hermitian-Toeplitz determinants of functions in the class of Ozaki close-to-convex functions, together with a sharp bound for the Zalcman functional J 2 , 3 ( f ) .