In this paper, we give an upper bound of Hankel determinant of (H 2 (1)) for the classes of M (α), α ∈ C. Also, for M (α), we obtain a sharp estimate for the classical Fekete-Szegö inequality. That is, we will get a sharp upper bound for the Hankel determinant H 2 (1) = c 3 − c 2 2. Moreover, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.