Hankel Determinant on the Class of Bazilevic Functions Related to Bernoulli Lemniscate
Marjono, Sa^adatul Fitri, Ratno Bagus, E.W., and Ni Made Asih

1 Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya,
Malang, Indonesia-
2 Department of Mathematics, Faculty of Mathematics and Natural Sciences, Univesity of Udayana,
Indonesia.

Abstract

In this research, we find the Hankel Determinant for the class Bazilevic Function B1(alpha,delta) related to the Bernoulli Lemniscate function on D = {z : |z| < 1}. We obtain the upper bounds of the determinant H2(1), H2(2), and H2(1) by considering its invers function. We used the Charateodory-Toeplitz Lemma about sharp inequalities for functions with positive real part.

Keywords: Bazilevic functions, Bernoulli Lemniscate, Subordination, Hankel determinant

Topic: Complex Analysis