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

Let f be analytic in D = {z is an element of C : vertical bar z vertical bar < 1}, and be given by f(z) = z + Sigma(infinity)(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).

Automated summary

This article explores sharp bounds for multiple determinants of functions in the class of Ozaki close-to-convex functions, as well as a sharp bound for the Zalcman functional J(2,3)(f).