Coefficient problems for starlike functions associated with a petal shaped domain

Abstract: In the present investigation, we consider a subclass of starlike functions associated with a petal shaped domain, recently introduced and defined by $$\mathcal{S}^{{*}_{\rho}:={f\in} \mathcal{A}:zf&#39;(z)/f(z) \prec 1+\sinh^{-1} z}.$$ We establish certain coefficient related problems such as sharp first five coefficient bounds along with sharp second and third order Hankel determinants for $\mathcal{S}<sup>{*}_{\rho}$. Also, sixth and seventh coefficient bounds are estimated to obtain the fourth Hankel determinant bound for the same class.