Abstract This article comprises the study of class S E ∗ $\mathcal{S}_{E}^{\ast }$ that represents the class of normalized analytic functions f satisfying ς f ′ ( z ) / f ( ς ) ≺ sec h ( ς ) ${\varsigma \mathsf{f}}^{\prime }(z)/\mathsf{f}( {\varsigma })\prec \sec h ( \varsigma ) $ . The geometry of functions of class S E ∗ $\mathcal{S}_{E}^{\ast }$ 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 S E ∗ $\mathcal{S}_{E}^{\ast }$ . We also investigate the same sharp results for inverse coefficients.
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