In this paper, we give an upper bound of Hankel determinant of (H2(1)) for
the classes of M(?), ? ? C. Also, for M(?), we obtain a sharp estimate for
the classical Fekete-Szeg? inequality. That is, we will get a sharp upper
bound for the Hankel determinant H2(1) = c3 ? c22. 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.