Coefficient problems for starlike functions associated with a petal shaped domain

TL;DR

This paper studies a subclass of starlike functions linked to a petal-shaped domain, establishing sharp bounds on coefficients and Hankel determinants to understand their geometric properties.

Contribution

It introduces and analyzes the class *_{ ho} of starlike functions, providing sharp bounds on coefficients and Hankel determinants, which are new results in this context.

Findings

Sharp bounds for first five coefficients.

Sharp second and third order Hankel determinants.

Estimated bounds for sixth and seventh coefficients.

Abstract

In the present investigation, we consider a subclass of starlike functions associated with a petal shaped domain, recently introduced and defined by $$\mathcal{S}^{*}_{\rho}:=\{f\in \mathcal{A}:zf'(z)/f(z) \prec 1+\sinh^{-1} z\}.$$ We establish certain coefficient related problems such as sharp first five coefficient bounds along with sharp second and third order Hankel determinants for $\mathcal{S}^{*}_{\rho}$. Also, sixth and seventh coefficient bounds are estimated to obtain the fourth Hankel determinant bound for the same class.