The second Hankel determinant for starlike and convex functions of order alpha

In recent years, the study of Hankel determinants for various subclasses normalised univalent functions f∈S given by f(z)=z+∑n=2∞anzn D={z∈C:|z|<1} has produced many interesting results. The main focus interest been estimating second determinant form H2,2(f)=a2a4−a32. A non-sharp bound H2,2(f) when f∈K(α), α∈[0,1) consisting convex order α was found Krishna and Ramreddy (Hankel starlike alpha. Tbil Math J. 2012;5:65–76), later improved Thomas et al. (Univalent functions: a primer. Berlin: De Gruyter; 2018). this paper, we give sharp result. Moreover, obtain results H2,2(f−1) inverse f−1 f∈S∗(α), class α. Thus, in paper complete set problems f classes S∗(α), K(α), Sβ∗ Kβ, where Kβ are, respectively, strongly starlike, β.