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 $${\mathcal{S}}_{\rho }^{\ast }:=\{f\in \mathcal{A}:z{f}^{\prime }(z)/f(z)\prec 1+{\sinh }^{-1}z\}.$$ We establish certain coefficient related problems such as sharp first five coefficient bounds along with sharp second and third order Hankel determinants for ${\mathcal{S}}_{\rho }^{\ast }$. Also, sixth and seventh coefficient bounds are estimated to obtain the fourth Hankel determinant bound for the same class.