Sharp coefficient inequalities of starlike functions connected with secant hyperbolic function

Abstract

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