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

Abstract

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∈N. The majority of bounds is sharp.