TY - JOUR
T1 - Third Hankel Determinant for the Inverse of Starlike and Convex Functions
AU - Guo , Dong
AU - Ao , En
AU - Tang , Huo
AU - Xiong , Liangpeng
JO - Communications in Mathematical Research
VL - 4
SP - 354
EP - 358
PY - 2019
DA - 2019/12
SN - 35
DO - http://doi.org/10.13447/j.1674-5647.2019.04.07
UR - https://global-sci.org/intro/article_detail/cmr/13563.html
KW - analytic function, third Hankel determinant, inverse of starlike function, inverse of convex function.
AB - Denote $\cal S$ to be the class of functions which are analytic, normalized
and univalent in the open unit disk $\mathbb U=\{z\colon |z|<1\}$. The important subclasses
of $\cal S$ are the class of starlike and convex functions, which we denote by $\cal S^*$
and $\cal C$.
In this paper, we obtain the third Hankel determinant for the inverse of functions
$f(z)=z+\sum\limits_{n=2}^{\infty}a_nz^n$ belonging to $\cal S^*$
and $\cal C$.