SOME RESULTS CONCERNED WITH HANKEL DETERMINANT

Abstract

In this paper, we discuss different versions of the boundary Schwarz lemma and Hankel determinant for K (alpha) class. Also, for the function f(z) = z + c(2)z(2) + c(3)z(3) + center dot center dot center dot defined in the unit disc such that f is an element of X(alpha), 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+alpha and f '(z(0)) = 1/1+alpha . That is, we shall give an estimate below |f ''(z(0))| according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and z(1) not equal 0. The sharpness of this inequality is also proved.