Coefficient problems for starlike functions associated with a petal shaped domain

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

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