Sharp Bounds of Hankel Determinant on Logarithmic Coefficients for Functions Starlike with Exponential Function

Abstract

Using the Lebedev–Milin inequalities, bounds on the logarithmic coefficients of an analytic function can be transferred to estimates on coefficients of the function itself and related functions. From this fact, the study of logarithmic-related problems of a certain subclass of univalent functions has attracted much attention in recent years. In our present investigation, a subclass of starlike functions Se* connected with the exponential mapping was considered. The main purpose of this article is to obtain the sharp estimates of the second Hankel determinant with the logarithmic coefficient as entry for this class.