Sharp coefficient inequalities of starlike functions connected with secant hyperbolic function

This article comprises the study of class ${\mathcal{S}}_E^{\ast }$ $\mathcal{S}_{E}^{\ast }$ that represents the class of normalized analytic functions f satisfying $\varsigma {\mathsf{f}}^{\prime }(z)/\mathsf{f}(\varsigma )\prec sech(\varsigma )$ ${\varsigma \mathsf{f}}^{\prime }(z)/\mathsf{f}( {\varsigma })\prec \sec h ( \varsigma ) $ . The geometry of functions of class ${\mathcal{S}}_E^{\ast }$ $\mathcal{S}_{E}^{\ast }$ is star-shaped, which is confined in the symmetric domain of a secant hyperbolic function. We find sharp coefficient results and sharp Hankel determinants of order two and three for functions in the class ${\mathcal{S}}_E^{\ast }$ $\mathcal{S}_{E}^{\ast }$ . We also investigate the same sharp results for inverse coefficients.