Affiliation:
1. Department of Mathematics , Kyungsung University , Busan 48434 , Korea
2. Department of Mathematics , Lublin University of Technology , Nadbystrzycka 38D, 20-618 Lublin , Poland
Abstract
Abstract
In recent years, the problem of estimating Hankel determinants has attracted the attention of many mathematicians. Their research have been focused mainly on deriving the bounds of
H
2
,
2
{H_{2,2}}
or
H
3
,
1
{H_{3,1}}
over different subclasses of
𝒮
{\mathcal{S}}
. Only in a few papers third Hankel determinants for non-univalent functions were considered. In this paper, we consider two classes of analytic functions with real coefficients. The first one is the class
𝒯
{\mathcal{T}}
of typically real functions. The second object of our interest is
𝒦
ℝ
(
i
)
{\mathcal{K}_{\mathbb{R}}(i)}
, the class of functions with real coefficients which are convex in the direction of the imaginary axis. In both classes, we find lower and upper bounds of the third Hankel determinant. The results are sharp.
Subject
Applied Mathematics,General Mathematics
Reference16 articles.
1. A. A. Amourah, F. Yousef, T. Al-Hawary and M. Darus,
On H3(p)H_{3}(p) Hankel determinant for certain subclass of p-valent functions,
Ital. J. Pure Appl. Math. 37 (2017), 611–618.
2. D. Bansal, S. Maharana and J. K. Prajapat,
Third order Hankel determinant for certain univalent functions,
J. Korean Math. Soc. 52 (2015), no. 6, 1139–1148.
3. R. Bucur, D. Breaz and L. Georgescu,
Third Hankel determinant for a class of analytic functions with respect to symmetric points,
Acta Univ. Apulensis Math. Inform. 42 (2015), 79–86.
4. P. L. Duren,
Univalent Functions,
Springer, New York, 1983.
5. B. Kowalczyk, A. Lecko, M. Lecko and Y. J. Sim,
The sharp bound of the third Hankel determinant for some classes of analytic functions,
Bull. Korean Math. Soc. 55 (2018), no. 6, 1859–1868.
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