ESTIMATES OF SECOND AND THIRD HANKELDETERMINANTS FOR BAZILEVIC FUNCTION OF ORDERGAMMA

Abstract

In the recent time, the study of Bazilevic functions became so popular that researchers, especially in Geometric Function Theory, have had to study different subclasses of Bazilevic functions in different directions. However, their study seem to lack full stamina addressing relevant connections of Bazilevic functions to some properties such as coefficient bounds, sharp bounds of the Fekete-Szego functional as well as the Hankel determinants for functions belonging to some specific subclasses of Bazilevic functions. Consequently, in this article, with the aid of Salagean derivative operator, the author derived the Bazilevic class T α n (γ), of order γ, type α, via the convolution of the fractional analytic function g(z) α and the normalized univalent function f(z) in the open unit disk. In the sequel, sharp bounds on the Taylor-Maclaurin coefficients |ak(α)| for functions belonging to the aforementioned class were obtained while the relationship of these bounds to the classical Fekete-Szego inequality H2(1) and Hankel determinants H2(2) and H3(1) were established using a clear Mathematical approach. Some of the consequences of the results so obtained were discussed as corollaries.