Bounds for the second Hankel determinant of certain univalent functions

Abstract

The estimates for the second Hankel determinant a 2 a 4 -a 2 3 of the analytic function f (z) = z + a 2 z 2 + a 3 z 3 + · · · , for which either zf (z)/f (z) or 1 + zf (z)/f (z) is subordinate to a certain analytic function, are investigated. The estimates for the Hankel determinant for two other classes are also obtained. In particular, the estimates for the Hankel determinant of strongly starlike, parabolic starlike and lemniscate starlike functions are obtained.

Third Hankel Determinants for Subclasses of Univalent Functions

“…They got the bounds: 1, 1/8 and 4/9, respectively. For the class S * (ϕ) of Ma-Minda starlike functions, the exact bound of the second Hankel determinant was obtained by Lee et al [5]. The proof of the result |H 2 (2)| ≤ 1 for the class C of close-to-convex functions can be found in the paper [15] by Selvaraj and Kumar.…”

On the Fekete-Szegö type functionals for starlike and convex functions

“…The investigation of Hankel determinants for analytic functions was started by Pommerenke (see [11,12]). Following Pommerenke, many mathematicians published their results concerning the second Hankel determinant for various classes of univalent functions (see, for example, [2,3,5,8,10]) or multivalent functions (see [9]). The bounds of a 2 a 4 −a 3 2 for typically real functions were presented in [14].…”

Coefficient Inequalities of Second Hankel Determinants for Some Classes of Bi-Univalent Functions

“…... P P, pw P ∆q. Now, equating the coefficients in (14) and (15) Now from (16) and (19) we get c 1 "´d 1 (22) and…”