Estimates for Analytic Functions Connected with Hankel Determinant

Abstract

We give an upper bound of the first-order Hankel determinant (H-2(1)) for the classes of analytic functions. In addition, an estimate with Hankel determinant from below is given for the second angular derivative of an analytic function f(z) . For new inequalities, we used the results obtained for Jack's lemma and Hankel's determinant. Moreover, in a class of analytic functions on the unit disc, the estimates of the modulus of angular derivative from below are obtained under the assumption of existence of an angular limit on the boundary point.