On $H_3(1)$ Hankel determinant for some classes of univalent functions

Focus in this paper is on the Hankel determinant, $H_3(1)$, for the well-known classes of bounded-turning, starlike and convex functions in the open unit disk $E=\{z\in \mathbb{C}\text{\hspace{0.17em}⁣}:\mathrm{\mid }z\mathrm{\mid }<1\}$. The results obtained complete the series of research works in the search for sharp upper bounds on $H_3(1)$ for each of these classes.