Hankel Determinants for Univalent Functions Related to the Exponential Function

Recently, two classes of univalent functions were introduced and studied. A function f is in if it is analytic in the unit disk, f(0)=f '(0)-1=0. On the other hand, if and only if. Both classes are symmetric, or invariant, under rotations. In this paper, we solve a few problems connected with the coefficients of functions in these classes. We find, among other things, the estimates of Hankel determinants: All these estimates improve the known results. Moreover, almost all new bounds are sharp. The main idea used in the paper is based on expressing the discussed functionals depending on the fixed second coefficient of a function in a given class.