Sharp bounds on the third Hankel determinant for the Ozaki close-to-convex and convex functions.

Our main purpose in this paper is to obtain certain sharp estimates of the third Hankel determinant for the class ℱ of Ozaki close-to-convex functions. This class was introduced by Ozaki in 1941. Functions in ℱ are not necessarily starlike but are convex in one direction and so are close-to-convex. We prove that the sharp bounds of ℋ3,1(f) and ℋ3,1(f−1) for f ∈ ℱ are all equal to 1/16. We also calculate the sharp bounds of the third Hankel determinant with entry of coefficients on the inverse of convex functions. [ABSTRACT FROM AUTHOR]