Preprint Article Version 1 This version is not peer-reviewed

# The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions with Real Coefficients

Version 1 : Received: 15 July 2019 / Approved: 17 July 2019 / Online: 17 July 2019 (08:41:14 CEST)

A peer-reviewed article of this Preprint also exists.

Kwon, O.S.; Sim, Y.J. The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions with Real Coefficients. Mathematics 2019, 7, 721. Kwon, O.S.; Sim, Y.J. The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions with Real Coefficients. Mathematics 2019, 7, 721.

Journal reference: Mathematics 2019, 7, 721
DOI: 10.3390/math7080721

## Abstract

Let ${\mathcal{SR}}^*$ be the class of starlike functions with real coefficients, i.e., the class of analytic functions $f$ which satisfy the condition $f(0)=0=f'(0)-1$, Re{z f'(z) / f (z)} > 0, for $z\in\mathbb{D}:=\{z\in\mathbb{C}:|z|<1 \}$ and $a_n:=f^{(n)}(0)/n!$ is real for all $n\in\mathbb{N}$. In the present paper, the sharp estimates of the third Hankel determinant $H_{3,1}$ over the class ${\mathcal{SR}}^*$ are computed.

## Subject Areas

starlike functions; Hankel determinant; Carathéodory functions; Schwarz functions