Estimates concerned with Hankel determinant for M(α) class

Abstract

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.

Sharp Coefficient Bounds for a Subclass of Bounded Turning Functions with a Cardioid Domain

“…The upper bounds of H q,n ( f ) have been investigated for different subclasses of univalent functions. By applying Schwarz Lemma [15,16], Selin Aydino glua and Bülent Nafi Örnek [17] determined the sharp bounds of Hankel determinant H 2,1 ( f ) = a 3 − a 2 2 for the class M α , defined by the condition f ∈ A and…”