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

中文翻译：

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与割双曲函数相关的星型函数的锐系数不等式

本文包括类 $\mathcal{S}_{E}^{\ast }$ 的研究，该类表示满足 ${\varsigma \mathsf{f}}^{\prime }(z 的归一化解析函数 f 类)/\mathsf{f}( {\varsigma })\prec \sec h ( \varsigma ) $ . $\mathcal{S}_{E}^{\ast }$ 类函数的几何形状是星形的，它被限制在正割双曲函数的对称域内。我们发现 $\mathcal{S}_{E}^{\ast }$ 类中的函数的尖锐系数结果和尖锐的二阶和三阶汉克尔行列式。我们还研究了逆系数的相同尖锐结果。