![]() |
![]() |
ETNA - Electronic Transactions on Numerical Analysis
|
![]() |
Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
![]() |
|
DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
|
ETNA - Electronic Transactions on Numerical Analysis, pp. 568-581, 2023/11/29
In this paper, we apply the differential evolution algorithm as a new approach to solve some coefficient problems within Geometric Function Theory. We find sharp bounds for the determinant of the Hankel matrix $H_{4,1}(f)$ and the determinants of all its sub-matrices for the class of starlike functions, i.e., for the class of all analytic injective functions $f$ in the unit disk $\mathbb{D}:= \{ z\in\\mathbb{C} : |z| <1\}$ normalized by $f(0)=f\'(0)-1=0$ such that $f(\Bbb D)$ is a starlike set with respect to the origin. In addition, a relevant conjecture regarding some coefficient functionals related to the Zalcman functional is formulated.
Keywords: differential evolution algorithm, Hankel determinant, starlike function, Carathéodory class and Zalcman functional