Sharp coefficient inequalities of starlike functions connected with secant hyperbolic function

Abstract This article comprises the study of class S₄^ S E ∗ that represents the class of normalized analytic functions satisfying f^ (z) /f () h () ς f ′ (z) / f (ς) ≺ sec h (ς). The geometry of functions of class S₄^ 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 S₄^ S E ∗. We also investigate the same sharp results for inverse coefficients.