Improved Upper Bounds of the Third-Order Hankel Determinant for Ozaki Close-to-Convex Functions

Abstract

LetN be the class of functions that convex in one direction and M denote the class of functions zf′(z), where f∈N. In the paper, the third-order Hankel determinants for these classes are estimated. The estimates of H3,1(f) obtained in the paper are improved.

Hankel Determinant for a Subclass of Starlike Functions with Respect to Symmetric Points Subordinate to the Exponential Function

“…After that, many papers focused on the upper-bound estimates of the second-order Hankel determinants H 2,1 and H 2,2 [22][23][24]. Recently, many scholars [25][26][27][28][29][30] have investigated the third-order Hankel determinant. Some sharp upper-bound estimates of the Hankel determinant for a subclass of univalent analytic functions were obtained via complex calculations.…”