Hankel Determinants for the Logarithmic Coefficients of a Subclass of Close-to-Star Functions

Abstract

Suppose that ST1 is a class of close-to-star functions. In this paper, we investigated the estimate of Zalcman functional on the logarithmic coefficients and the third Hankel determinant for the class ST1 with the determinant entry of logarithmic coefficients. Also, we obtained the sharp bounds of Zalcman functional J2,4f and J3,3f for the class ST1.