Communications of the
Korean Mathematical Society CKMS

In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, Briot-Bouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.

Keywords: Briot-Bouquet differential subordination, hyperbolic cosine function, partial sums, starlike functions, third Hankel determinants

MSC numbers: 30C45, 30C50