Hankel Determinants of Normalized Analytic Functions Associated with Hyperbolic Secant Function

Abstract

In this paper, we consider a subclass of normalized analytic functions associated with the hyperbolic secant function. We compute the sharp bounds on third- and fourth-order Hermitian–Toeplitz determinants for functions in this class. Moreover, we determine the bounds on second- and third-order Hankel determinants, as well as on the generalized Zalcman conjecture. We examine a Briot–Bouquet-type differential subordination involving the Bernardi integral operator. Finally, we obtain a univalent solution to the Briot–Bouquet differential equation, and discuss the majorization property for such function classes.

Keywords

• Briot–Bouquet differential subordination
• Hermitian–Toeplitz and Hankel determinants
• hyperbolic secant function
• starlike functions
• majorization