Affiliation:
1. Department of Mathematics Faculty of Science and Letters Kafkas University Kars Turkey
Abstract
Abstract
In this paper, we introduce and investigate the following subclass
1
+
1
γ
z
f
′
(
z
)
+
λ
z
2
f
″
(
z
)
λ
z
f
′
(
z
)
+
(
1
−
λ
)
f
(
z
)
−
1
≺
φ
(
z
)
0
≤
λ
≤
1
,
γ
∈
C
∖
{
0
}
$$\begin{array}{}
\displaystyle 1+\frac{1}{\gamma }\left( \frac{zf'(z)+\lambda z^{2}f''(z)}{\lambda zf'(z)+(1-\lambda )f(z)}-1\right) \prec
\varphi (z)\qquad\left( 0\leq \lambda \leq 1,\gamma \in
\mathbb{C}
\smallsetminus \{0\}\right)
\end{array} $$
of analytic functions, φ is an analytic function with positive real part in the unit disk 𝔻, satisfying φ (0) = 1, φ '(0) > 0, and φ (𝔻) is symmetric with respect to the real axis. We obtain the upper bound of the second Hankel determinant | a2a4−
a
3
2
$\begin{array}{}
a^2_3
\end{array} $
| for functions belonging to the this class is studied using Toeplitz determinants. The results, which are presented in this paper, would generalize those in related works of several earlier authors.
Reference14 articles.
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4. Duren, P. L.: Univalent Functions. Grundlehren Math. Wiss. 259, Springer, New York, 1983.
5. Fekete, M.—Szegö, G.: Eine Bemerkung uber ungerade schlichte Funktionen, J. London Math. Soc. 8 (1933), 85–89.
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