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

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