Upper Bounds of the Third Hankel Determinant for Close-to-Convex Functions

In this paper, the third Hankel determinant for the class N of functions convex in one direction is estimated. An analogous problem is solved for a subclass of N consisting of functions with real coefficients. Additionally, this determinant for odd functions in N is estimated. Moreover, similar results are obtained in the relative class M consisting of functions zf'(z), where f is an element of N . The majority of bounds is sharp.

Automated summary

This paper estimates the third Hankel determinant for the class N of functions convex in one direction and solves an analogous problem for a subclass of N consisting of functions with real coefficients. Additionally, the determinant for odd functions in N and functions zf'(z) in the relative class M are also estimated, with most of the results being sharp.