The Bound of the Hankel Determinant of the Third Kind for Starlike Functions

By Oh Sang Kwon, Adam Lecko, Young Jae Sim. Bulletin of the Malaysian Mathematical Sciences Society, 2018

118 citations recorded by the source corpus.

In the present paper, the estimate of the third Hankel determinant $$\begin{aligned} \begin{aligned} H_{3,1}(f)&= \begin{vmatrix} a_{1}&a_{2}&a_{3} \\ a_{2}&a_{3}&a_{4} \\ a_{3}&a_{4}&a_{5} \end{vmatrix} \end{aligned} \end{aligned}$$H3,1(f)=a1a2a3a2a3a4a3a4a5for the class of starlike functions, i.e., for the class of analytic functions f standardly normalized such that $${{\mathrm{Re}}}(zf'(z)/f(z)) > 0,\ z\in {{\mathbb {D}}}:=\{z \in {\mathbb {C}} : |z|<1\},$$Re(zf′(z)/f(z))>0,z∈D:={z∈C:|z|<1}, is improved.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/66b1540b216d0109c780a8601591fa56421f4acb

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In Applied Mathematics

1. S. Banga
2. Muhammad Arif
3. Lei Shi
4. Sanjay Kumar
5. Nak Eun Cho

In Geometry and Topology

1. S. Banga
2. Muhammad Arif
3. Shehzad Hussain
4. Lei Shi
5. Sanjay Kumar
6. Nak Eun Cho

Citations in the corpus

• The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛* (2019, background): “[15] improved the estimate of the third Hankel determinant for starlike functions.”
• A Study of Third Hankel Determinant Problem for Certain Subfamilies of Analytic Functions Involving Cardioid Domain (2019, background): “[38] improved the bound of Zaprawa for f ∈ S∗ and proved that |H3,1 ( f )| ≤ 8/9, but it is not yet the best possible.”