Some Results Concerned with Hankel Determinant

Abstract

. In this paper, we discuss different versions of the boundary Schwarz lemma and Hankel determinant for K ( α ) class. Also, for the function f ( z ) = z + c 2 z 2 + c 3 z 3 + · · · defined in the unit disc such that f ∈ K ( α ), we estimate a modulus of the angular derivative of f ( z ) function at the boundary point z 0 with f ( z 0 ) = z 0 1+ α and f 0 ( z 0 ) = 1 1+ α . That is, we shall give an estimate below | f 00 ( z 0 ) | according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and z 1 6 = 0. The sharpness of this inequality is also proved.