New upper bounds of the third Hankel determinant for some classes of univalent functions

TL;DR

This paper provides improved upper bounds for the third Hankel determinant in certain classes of univalent functions, advancing understanding of their coefficient constraints.

Contribution

It introduces new upper bounds for the third Hankel determinant for specific univalent function classes and conjectures the exact sharp bounds.

Findings

Improved upper bounds for the third Hankel determinant.

Proposed conjecture for the sharp bounds.

Analysis applicable to various univalent function classes.

Abstract

In this paper we give improved, probably not sharp, upper bounds of the Hankel determinant of third order for various classes of univalent functions and conjecture the sharp one.