Estimates Concerned with Hankel Determinant for M (?) Class

Abstract

In this paper, we give an upper bound of Hankel determinant of (H2(1)) for the classes of M (alpha), alpha is an element of C. Also, for M (alpha), we obtain a sharp estimate for the classical Fekete-Szego center dot 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.