# On third Hankel determinants for subclasses of analytic functions and close-to-convex harmonic mappings

## TL;DR

This paper establishes upper bounds for the third Hankel determinants across various subclasses of analytic functions and explores new results on close-to-convex harmonic mappings, linking these findings to existing literature.

## Contribution

It provides new upper bounds for third Hankel determinants for multiple subclasses and introduces results on a novel subclass of close-to-convex harmonic mappings.

## Key findings

- Upper bounds for third Hankel determinants for starlike, convex, and bounded turning functions.
- New results on a subclass of close-to-convex harmonic mappings.
- Connections to existing literature are discussed.

## Abstract

In this paper, we obtain the upper bounds to the third Hankel determinants for starlike functions of order $\alpha$, convex functions of order $\alpha$ and bounded turning functions of order $\alpha$. Furthermore, several relevant results on a new subclass of close-to-convex harmonic mappings are obtained. Connections of the results presented here to those that can be found in the literature are also discussed.